 We are talking about axial flow turbines, axial flow turbines that are used in aircraft jet engines. They are also of course, called gas turbines in so far as they use the hot gases that come from the combustion chamber to produce work. And as we have discussed before, this work is essentially used to run the compressor of a typical aircraft engine. Now, in the last class, we had a quick look at what a basic axial flow turbine looks like, how does it work and how does it works, which are done by axial flow turbines can be quantified in terms of work done, in terms of efficiency, so on and so forth. Today, we will try to take a look at number of things. One is how such turbines are characterized. You have done in your compressor chapter that typical compressors are also characterized and they are also often simply referred to as characteristic maps. So, we will take a look at such a characteristic map today. We will also take a look at what it involves in multistaging of turbines. As we have discussed, if the aggregate amount of work that needs to be supplied to run the compressor or the fan of a turbofan or running a propeller of a turboprop requires large amount of work to be done by the turbine, quite often it may not be possible to do it in one stage of turbine, in which case multistaging often is required. And we will take a look at what this multistaging involves and typically much of this multistaging may involve multispooling. That means, we will have two spools or two shafts, two concentric shafts as we have again discussed before. And those two spools, how do they actually look like, how do they operate and what happens to their characteristics? So, we will take a look at some of these issues and then afterwards we will take a look at the turbine blade cooling technology. Because this is the technology that has dominated the turbine development over last 50 years, much of the development of axial flow turbine specially with reference to aircraft engines has been around the blade cooling because simple thermodynamics have already told us in very clear terms that higher the entry temperature to the turbine, higher is the work extraction capability of the turbine. And also it impacts on the overall efficiency of the cycle, the jet engine cycle and higher the temperature, higher is the efficiency of such a cycle and this efficiency shows up in the form of fuel efficiency. So, higher turbine entry temperature or higher temperature coming from the combustion chamber does mean double benefit more work by the turbine and more efficiency of the working engine cycle. Now, to take full benefit of this high temperature, it is necessary to protect the turbines from completely getting burnt or charred because that can happen even as we use high temperature materials, the turbine blades are quite amenable to getting completely charred if such high temperatures persist for quite some time. And hence it is required to have certain cooling technologies incorporated in the turbine blades for continuous cooling of these blades. And hence these cooling technologies are essentially the lifeline of the turbine blades, without these cooling technologies incorporated in the turbine blades, these blades actually would not survive for sometimes more than a few minutes. So, we are talking about a cooling technology that is integral to the development of axial flow turbines as used in aircraft engines. So, let us take a look at some of these issues related to axial flow turbines specifically as used in aircraft engines. So, as I mentioned today we will be taking a look at three things the characteristics, the multistaging of the turbines and the blade cooling technology used in the modern aircraft engines. Let us start with the characteristics of axial flow turbines. Now, axial flow turbines do have characteristics similar to that of compressors axial flow compressors or centrifugal flow compressors that you have done before and they are called characteristics simply because they actually characterize a particular turbine. Every turbine, every turbine has its own characteristics, there is nothing like a generalized characteristics of all kinds of turbines. So, every turbine needs to be characterized immediately after its creation, immediately after it is designed and made it needs to be characterized. The first characterization is normally done in our days in a computerized manner. However, that needs to be also validated through rigged testing and once the rigged testing is over, we have a certain characteristic map that characterizes that particular axial flow turbine which would then be used for characterizing not only characterizing the turbine, but matching this turbine with rest of the engine that goes on the aircraft and this characteristic map would also be used for control of the turbine, the control of the engine along with the various control rules that govern the control of the engine along with the control of the aircraft. So, these characteristics are extremely important for operation of the turbine in so far as operation of the entire jet engine and as a result of which this characteristic map is one of the first things that you would need to have with you immediately after the turbine is created. So, let us take a look at what a typical characteristic map of axial flow turbine looks like and what does it actually mean. Now, the turbine characteristics as given in this map is typically drawn with a mass flow parameter on the y axis and the pressure ratio across the turbine as the x axis. Now, this is slightly different from the way it is done for example, in case of compressors as we have done before. In case of compressors typically the pressure ratio is shown on the y axis and the mass flow parameter as it is shown here is shown in the x axis. So, in case of turbine this is switched around the two axis are essentially switched around also notice that we are using a normalized mass flow parameter. So, we are not using the mass flow directly we are using a normalized mass flow parameter normalized by the temperature and pressure of the turbine of the operating point of the turbine or at the entry to the turbine. The present map actually shows m dot into root over t 0 i divided by p 0 i because we have drawn the characteristics with two different sets of t 0 and p 0. One is t 0 1 p 0 1 with reference to the entry of the axial flow turbine and then t 0 2 p 0 2 which is the exit of the axial flow turbine. Also notice that we are using the total parameters the total temperature and total pressure to signify or normalize this mass flow parameter and as you see it is done with reference to two different stations. One is the entry station of the turbine another is the exit station of the turbine and p 0 2 by p 0 1 is the pressure ratio across the turbine as you know there is going to be pressure drop across the turbine. So, essentially this is the pressure drop ratio across the turbine. Now what happens is if you show it with reference to let us say the entry point parameters of the turbine the mass flow parameter the characteristic map would typically follow this red line and at a certain point of time it will simply become a flat line and that is because somewhere over here the flow actually goes choking. So, a typical aircraft gas turbine engine operates most of the time in a choked manner. Now this is the reason is the pressure ratio that operates across a typical turbine is often higher than the required theoretical choking pressure ratio and this is something which most of the aircraft gas turbines are deliberately designed for and as a result of which most of the aircraft gas turbines specially the early gas turbines the first one or two stages of the gas turbine are invariably choked. This means that typical design point at which the turbine is most likely to operate is actually operating under choked condition and thus that is shown here in the red blob it shows that the flow is actually choked through the turbine that means it is reached maximum mass flow if you continue to increase your pressure drop across the turbine further and further mass flow through this turbine is not going to increase anymore and that means that the mass flow through the entire engine has now reached a maximum it cannot go above this mass flow anymore because somewhere in the engine and in this case across this particular turbine the flow has got choked it cannot increase mass flow anymore. This is typically the condition under which most aircraft gas turbines actually indeed operate and hence even if you increase the pressure ratio you are not going to get more mass flow if you increase the pressure ratio as we know you can indeed get more work done as we have done in the cycle analysis we can get more work done but you are not going to get more mass flow through the turbines anymore. On the other hand if the characteristics is actually drawn with reference to the exit flow conditions we see this dotted line over here it continues to rise with the pressure rise and as a result of which the design point which is shown here is already choked flow condition would now actually be somewhere over here where it is still a rising characteristic. Now this dotted line which is drawn with reference to the exit of the turbine can also be said to be the entry to the next stage of turbine if it is a multi-stage turbine. So, this corresponds to the next stage of a multi-stage turbine which we shall have a look at in a few minutes from now. So, it means that a flow which is choked under the entry flow conditions may indeed look unchoked if it is plotted against exit flow condition. Now this is what the turbine characteristics mean and we shall take a look at what it means when you have multi-stage turbines. Now multi-staging of the turbine is essentially done for two or three main reasons. One of the reason is that it is done to extract more aggregate energy or mechanical power which is needed either to run the compressor or to run fan or number of stages of fan whatever the engine configuration is and as a result the turbines are required to produce more work to be supplied to the compressor or a fan or a combination of compressors and fans. There is another reason why sometimes multi-staging is an important issue. The issue is that if each stage has to do more work and in aircraft engine typically it requires that the turbine is not very large in size. If you keep on increasing the number of stages the total amount of space that needs to be allotted to the turbines would go up, the length of the engine would go up, the weight of the engine would go up and many of these things are not really acceptable to an aircraft application or to an aircraft designer really speaking and as a result of which such turbines and such engines are unlikely to be accepted for aircraft applications. In such a case it is required that each of these stages are also highly loaded. Now when we talk about loading we are talking about aerothermodynamic loading. Some of these loading parameters are what we have talked about before in with reference to your cycle analysis. The loading essentially refers to the amount of work that it can do in a single stage across one row of rotor let us say and that is signified by the aerothermodynamic loading which means the typical aircraft gas turbine is typically much more aerothermodynamically loaded compared to any other kind of turbine or gas turbine which may be used in land based applications where the restriction of size and weight does not quite apply so stringently and as a result of this the aircraft gas turbines essentially need to be highly loaded even when they are multi stage. So multi staging may not be the only solution one has to go for aerothermodynamic loading which as we just saw means that the more and more stages are likely to be choked that mean they would be loaded to the maximum with reference to their working capability. There is a third reason why multi spouring is often resorted to in aircraft gas turbine engines. Quite often multi spilling is not necessary in land based gas turbine engines. Land based gas turbine engines are indeed much bigger and larger than aircraft engines. They produce much more power than aircraft engines but multi spilling is often not resorted to in land based engines and one of the reasons is in aircraft operation it has to work under various operating conditions during its flight, during takeoff, during climb, during cruise all these conditions require different kind of atmospheric conditions, different kind of working conditions in front of the turbine and as a result of which the turbines may be asked to or required to operate under different operating speeds or rotating speeds that means if you look at this multi stage turbine now we have an HP turbine and then we have a set of LP turbines. Now as we can see here the HP turbine has two stages stator rotor and then stator rotor as we have seen typical turbine stages made up of a stator and a rotor. So, we see here two stages of HP turbine and then we see here something like four stages of LP turbine stator rotor stator rotor etcetera and as a result of which we have a set of LP turbines. Now such a LP turbine in a aircraft engine would typically be designed to operate at a different rpm most notably it will be operating at a rpm substantially lower than that of the HP turbine. Typically HP turbine would be rotating at very high rpm of the order of 10000 rpm or more whereas LP turbine is most likely to operate at much lower rpm could be of the order of 7 or 8000 rpm or may be even lower than that because this LP turbine is most likely to be powering fans of a turbofan engine. Now fans of a turbofan engine as you have done earlier before actually are expected to operate under slightly lower rpm's than the high pressure compressors. The reason being the typical aircraft fans go supersonic at certain speeds operating speeds. However, very high supersonic speeds even today are not very comfortable both by the designer as well as by operational conditions and as a result the compressor and fan designers try to avoid very high supersonic operating speeds through these compressors. Now to restrict this speed operating fluid mechanical or fluid dynamic speed through these compressors the compressor rotating speed needs to be limited to certain values. So, the turbines which drive the compressors directly through a concentric shaft also need to conform to this restriction of rotating speeds and as a result of which LP turbines would need to be rotated at a somewhat lower speed than typical HP turbines. So, these are some of the fundamental reasons for multistaging and these reasons allow the aircraft designer a lot of flexibility in design lot of flexibility to the operation of the typical aircraft engine and these operational flexibilities are what needs to be designed into the aircraft engine gas turbine. Now gas turbines are designed to then have these flexibilities they are various operational loadings under various operating conditions they operate at various speeds under various operating conditions and also they can be made to operate under various kinds of temperatures which come from the combustion chamber. Because combustion chamber you can increase or decrease the combustion chamber delivery temperature by simply increasing or decreasing the fuel that is burnt in the combustion chamber. So, the turbine should also be able to operate at various incoming temperature levels along with various speeds and as a result of which the turbines would be operating under various loading conditions. So, all this needs to be built into the design of the axial flow turbine and this design should then conform to the need of the entire engine as you have done in cycle analysis and that engine would then be fit for going on an aircraft mission. Now, let us take a look at what happens if you have a multistage turbine and then this multistage turbine needs to again have a characteristic. Now, let us take a look at this multistage turbine characteristics see now you have a HP turbine and you also have a LP turbine. Now, this HP turbine characteristics we had a look at earlier and as we can see here the turbine is essentially let us say choked. Now, this choking condition corresponds to a exit condition over here which is shows a rising characteristic and then this is translated to the next map which is that of the LP turbine and this LP turbine now is operating at this condition which we can see now is also choked. So, the present design is such that the way it is operative the set of HP turbine let us you know conform to the earlier diagram we have a set of HP turbine we have a set of LP turbines. Now, this HP turbine let us say characteristics is representing the set of HP turbines and this LP turbine characteristic let us say is representing that set of LP turbines. Now, all of them together then it shows that while the HP turbine set is choked at the same time the LP turbine also looks choked when we take the exit condition of the LP turbine and the mass flow parameter normalized mass flow parameter is shown it shows that it shows a rising characteristic that means with varying pressure ratio it can continue to show rising characteristics. Now, these characteristics are essentially then show that both the turbines are capable of working under choked condition. However, if let us say under some operating condition the LP turbine is now required to operate at a lower operating speed rotating speed in which case it could actually get un choked it could get slightly un choked and then if you translate that slightly un choked condition to the HP turbine we will see that HP turbine is most likely to be still choked. So, if we translate some of the slightly un choked operating conditions of LP turbine back to HP turbine we will see that they are still choked condition. So, through the various operating conditions of LP turbine it is most likely that the HP turbine will continuously remain choked. On the other hand if we go to the right of the characteristic design point and look at these green points where LP turbine is operating at a higher pressure ratio that means it is now made to operate at a higher rotating speed it is fully choked now and corresponding to that the HP turbine will continue to remain choked not only it will continue to remain choked it will continue to remain operative under same operating condition that means its choked condition will remain exactly same as it was which means that under variable operating conditions of LP turbine where it can go down to even un choked or highly choked you know fully choked the HP turbine will continue to operate under stable single operating condition. Now, this is the important point that LP turbine may have variable operating conditions from un choked to choked whereas HP turbine through all these will continue to remain stable under one single choking operating condition. Now, this is how normally the HP and LP turbines are designed together they are matched together and we will probably have a look at some of these matching issues later on in the course of this lecture series. So, this is how multistaged turbine is often characterized. Let us take a look at what happens when you have multistaged turbine the inlet and outlet operating conditions can now be varied slightly. For example, we had a look at the velocity diagrams of the vector diagrams in which alpha 2 of course was the exit angle from the stator nozzle onto the rotor and what we see here that in the HP turbines the front stages the alpha 2 values can be very high because that is where we are looking at very high velocity choked flow fully choked flow condition as we have just seen and the flow has gone completely sonic may be slightly supersonic. On the other hand the last stages the flow may not be sonic may or may not be sonic and the angle is slightly on the lower side corresponding to the exit flow condition from the stator nozzle of that particular stage. The degree of reaction r x in turbines as we know typically they are on the lower side compared to what you have seen in the compressors the degree of reaction in turbines is substantially lower which means that more of static changes are occurring in the stator and less of them in the rotor and this is by design the static change that occurs in the rotor actually corresponds to the reaction turbine in a impulse turbine the reaction that we are showing here degree of reaction would indeed be 0. So, an impulse turbine has a 0 degree of reaction whereas, a reaction turbine typically as used in aircraft gas turbines would have positive values, but these values are nowhere near as high as you have seen in case of axial flow compressors. There also is a slight variation in the front stages in the HP stages the values are of the order of 0.2 to 0.25 whereas, in the later stages the values are slightly on the higher side that means more reaction is obtained from the LP stages whereas, in the HP stages the reaction force that is obtained through the reaction mechanism in the rotor is somewhat on the lower side and one of the reasons is the HP stages the flow is already of very high energy and as a result the work being performed through the impulse force is already of a very high order whereas, in the later stages the potential energy available in the LP turbines is somewhat of a lower order and hence an effort is made to obtain more from the reaction force because less is available from the impulse force for running of the turbine. The exit Mach number as we can see here from the front stages is not very high because it is coming with a low Mach number from the combustion chamber. So, in the front stages the exit Mach number is of the order of 0.25 or 0.35. Mind you this is Mach number is dependent on the local temperature. So, one has to factor in the local temperature to actually find out or figure out what the actual velocity would be. In case of turbojet and turbofan engines the LP stage or the last stage exit condition would probably show a Mach number of the order of 0.5 and this flow is indeed going into a nozzle where it will get subsequently even more accelerated through the nozzle to create the jet thrust. On the other hand if it is a turbo prop engine you normally endeavour to create more work out of the turbines to run the propeller and hence you do not like to have exit flow containing a lot of energy anymore and hence you extract maximum amount of work from the turbine and then let it go with a slightly actually higher Mach number because you are not trying to get a lot of nozzle thrust anymore. You simply want the flow to go out with a may be a very small amount of thrust creation. So, more of the work is being done through the propeller whereas in turbojet and turbofan the typical full jet engines you still have a nozzle as another component of the engine and that nozzle is going to create higher acceleration and a high velocity jet for thrust creation. The exit angle from the turbines typically in the front stages there is indeed no prescription of what the angle could be. It could be a little on the higher side because it is going into the later stages and it depends on the designer to create what angle he chooses to be the best possible angle. However, in the last stages one would like to see it going out with very low angle. The reason is you do not want a lot of wheel component or tangential component of the jet that is going out from the turbine because that component is not useful for thrust creation. Now, this is something known very well specially for aircraft gas turbine engines for a craft jet engines and hence you let the flow go out of the turbine with minimum possible angle or wheel angle. So, that it does not have a wastage of energy in the wheel component of the outgoing flow. Now, this is the situation that is normally kind of prescribed for typical aircraft gas turbines specially when you have multi staging of gas turbines meant for aircraft usage. These are prescriptions not very binding actual design values would vary from one kind of turbine to another. Now, let us take a look at various kinds of cooling mechanism that is normally used in various kinds of aircraft cooling, gas turbine cooling. Now, you see the gas turbines in aircraft typically are subject to very high temperature. In fact, as we have noted before in thermodynamics, it clearly states that if you have higher and higher entry temperature to turbine, you get more and more work extraction possibility. You also of course, get a higher cycle efficiency or engine efficiency reflected in the fuel efficiency. So, a high turbine temperature is something which every turbine designer for aircraft usage has been working on for over last 50 years and that entry temperature is going up all the time over the last 50 years. So, 50 years back the entry temperature to turbine was of the order of 1000 degree, 1000 degree centigrade or even lower about 850 degree centigrade about 1000 degree Kelvin. Today, that temperature is of the order of 18 to 1900 degree Kelvin and it is even now going up depending on the cooling technology that is available at hand. So, let us take a look at this history of cooling that has been going on for a period of almost little more than actually 50 years. Now, if you look at this diagram here, it shows the temperature which the turbines are being subjected to on the y axis and the chronological development over the years from 1950, when the jet engine started flying till today. Now, what it shows is that in the early years, the turbine blades were indeed uncooled. They were made of so called high temperature materials which are typically in conal and monal. These are nickel based alloys which have been used for gas turbines for over last 50 years. Now, these were used without any cooling technology in the early years and that allowed one to go may be up to something like 1150, 1200 degree Kelvin, but after that these blades would not survive. In fact, indeed if you increase the temperature from 1200 to 1300, the same blade would probably get charred in a matter of few minutes. You cannot possibly have turbines operating at that kind of temperature anymore. So, once the temperature crossed the 1000 centigrade mark, cooling became an absolute necessity for all kinds of aircraft engines. Now, what happens is you can see here in the early years, there were some simple cooling mechanism which was used in passing some cooling air through the blades and this introduction to blade cooling provided some relief and certain amount of increase in temperature could be easily achieved. Once that possibility was exhausted more and more and in those days it was simply called convection cooling because air was passed through the blade and so called cooled air passing through the blade took away some of the heat and the amount of cooling that could be achieved was of the order of 50 to 100 degrees only and that was sufficient to give the blades a reasonable life of the order of few thousand working hours. As I mentioned without that cooling, the blades would have got charred in a matter of 1 or 2 minutes. So, from 1 or 2 minutes the blades could be rendered a life of the order of few thousand working hours through this simple convection cooling only. However, as the designers wanted to go for higher and higher temperature, more and more sophisticated cooling techniques were required and some of these cooling techniques then came into the picture. These are we will have a look at some of these in a few minutes from now, but these are called film cooling and impingement cooling and these were added to the convection cooling. So, convection cooling as a fundamental cooling technology remained, but additional cooling technologies were added inside the blades. So, the inside of the blades become more and more complex and we will have a look at them in a few minutes now and as a result of which the cooling technique now available in actually involves at least three kinds of cooling, the film cooling, the impingement cooling and the convection cooling. A combination of these is what is normally used in many of the modern gas turbine engines. One of the futuristic things that people have been talking about for almost 30 40 years now is the transpiration cooling, but it is not really been you know incorporated in the blades as yet because it requires a new material technology development which is not happened. So, this has been extended and we have reached temperatures of the order of 2000 Kelvin which is of the order of 1700 degree centigrade as of today in turbine operation anything more than that indeed requires a jump in the cooling technology a new kind of cooling technology which people are still researching for the material technology also is being researched for. So, combination of new material technology and new cooling technology would hopefully take us to higher temperatures in the years to come. Now, the additional cooling technologies that I was talking about that is the additional film and impingement cooling essentially renders more life to the turbine blades. The life we are now talking about is in terms of according to present regulations of turbine usage it has to be of the order of something like 10000 working hours or running hours. Now, to render that kind of life with higher operating condition requires that you have very extensive cooling technology built into the typical turbine blades and this is what this combination cooling the film and impingement cooling is essentially trying to achieve that at such high temperatures the turbine blade without the cooling would have got charged in a matter of seconds. So, from getting charged in a matter of seconds to rendering a life of the order of something like 10000 working hours is what this cooling technologies have indeed achieved and this is what we are going to talk about in this lecture today. Now, let us take a look at what this cooling technology fundamentally involves when the gas flows over a turbine blade it creates a certain flow field around it and this fluid flow feel around actually involves a laminar flow around it and then it there is a transition from laminar and then the flow indeed becomes turbulent. So, most of the surface of a turbine blade actually experiences turbulent flow over it only the leading edge part of it experiences laminar flow around the leading edge area and then after that the flow transits to turbulent flow. Now, when the flow transits from laminar to turbulent flow it is heat transfer characteristic also changes in a laminar flow as the definition of laminar flow is known to you there is no mass or heat flux across the laminers of the flow which means the laminers segregate each other and hence those laminers do not allow any high temperature to flow in from the hot gas into the blade. However, at this stagnation point here when the flow indeed comes almost to a stagnation or theoretically to a stagnation the entire hot gas kinetic energy is now available in terms of potential energy. So, the total temperature at this point is equal to the static temperature and that is exactly what is indeed felt at this stagnation point. So, this stagnation point is indeed the hot spot of a typical gas turbine blade. Now, this hot spot is what everybody is most worried about and we shall see very soon how this hot spot is expected to be cooled or enable to be cooled through impingement cooling from inside. So, this stagnation point is one of the problems of heat transfer cooling of typical gas turbine blades after that the flow is laminar and as we can see the flow naturally does not provide a lot of heat transfer and then immediately afterward as the flow accelerates over this surface very fast this acceleration actually converts the flow from laminar flow to turbulent flow through this transition. Once the transition occurs and the flow has become turbulent the heat transfer across the laminers actually now start taking place. So, the hot gas now can easily pass on its heat to the turbine blades and the turbine blades could indeed get badly heated up and that can happen from both the surfaces from the upper surface as well as from the lower surface. Now, what we shall see now is that this heat transfer actually continuously changes over the blade surface. So, depending on the blade curvature of each of the surfaces the C p a coefficient of pressure over the blade surface is continuously changing. So, the velocity field over the surface is continuously changing and the local temperature is continuously changing that means the heat transfer coefficient is continuously changing. Now, this continuous change of local heat transfer coefficient means that you need to indeed provide differential cooling at different point of the turbine. We have just seen that the stagnation point is a hot spot. We also know that somewhere near the trailing edge there could be another local stagnation point which would indeed become another hot spot because the local temperature there would be equivalent to the stagnation temperature. There are many such areas over the gas turbine where the blade is extremely sensitive. The suction surface of the blade which actually participates more in the working of the gas turbine needs to be protected and as a result of this you need to provide differential cooling over this gas turbine surfaces. Let us see how this differential cooling can be provided, but before that we will have a definition of the heat transfer coefficient. Typical definition of the heat transfer coefficient is that the quantity of a heat transferred across from the gas to the blade let us say is divided by the surface area, the time that is available small t and the temperature differential between the hot gas and the surface. Now, if you have a cooled blade, the blade is continuously being cooled and as a result of which there is a continuous temperature differential between the hot gas and the blade surface and as a result of which there is a continuous heat flux across from the hot gas on to the blade surface and this heat flux need to be continuously taken away by the cooling method that is deployed inside the gas turbine. Now, this is the heat transfer coefficient one needs to cater to. Let us also take a quick look at what the temperature on a blade surface as felt by it could possibly be. The typical temperature felt by the blade is to begin with mean of T 0 1 plus T 0 2 that is the temperature across the blade row and the mean of that minus the kinetic head which is u mean square of the particular blade divided by twice of C p of the gas into 1 minus 2 into degree of reaction. Now, this provides that the kinetic head of the flow actually has a small negative effect on the temperature felt by the blade surface. So, it means that higher the temperature incoming into the turbine higher would be the temperature felt by the glass. Now, this is something which is what we are trying to cater to the turbine needs to work under high temperature conditions to extract more work on the other hand more the increase in free temperature more is the temperature felt by the blade and hence you need to provide more and more cooling. Now, this is something which we would need to bother about on the other hand if the work extraction capability of the turbine is enhanced T 0 2 at the end of the turbine would be actually lower in which case the mean of this would be lower and hence one can say that towards the trailing edge of the blade you would need probably less of cooling. So, these are some of the issues that the typical turbine blade cooling designer would have to deal with in designing the cooling technology. Typical turbine cooling technology as we have been talking about started with what is known as internal convection cooling. Now, let us take a look at how it actually works you have ribs like this inside the blade of a turbine cooling. We are showing here let us say a flat plate and inside the flat plate on the other side you have these ribs. Through the ribs if you if you pass cooling air what the cooling air does is when you have a hot gas passing over this plate this plate is continuously getting heated up and the cooling air passing through these ribs what we call internal convection cooling is continuously cooling the inner surface of this plate. So, the outer surface is getting heated up by the hot gas then there is a heat flux across the thickness of this plate and then the inner surface of the plate is continuously getting cooled by this cold air and as a result of which the heat does not accumulate anywhere it does not create a hot spot there is a continuous heat flux across the plate taken away by the cold air and as a result of which this hot plate is said to be continuously cooled by this internal cooling air convection. So, the convection of cold air inside of the hot plate provides a continuous cooling mechanism to this plate which is getting heated by the hot gas. The next method which came into being and which is used typically in front of the in the front side of the blade that is the internal side of the leading edge of a blade is the impingement cooling. Now, let us see how it actually works. So, you see you have the hot plate over here which is heated by the hot gas and then this hot gas is subjected to impingement from cold air from inside through these holes and these holes impinge on the inside of the hot air hot gas hot plate and then this hot plate is cooled from inside through the impingement of cooling air coming through these holes. So, this is called impingement cooling and this is what is deployed in many of the modern gas turbines specially the aircraft gas turbines specially near the leading edges. Let us take a look at some of the other cooling methods the film cooling which I talked about what it does is the cooling air is passed through a hole made actually in the plate in the blades actually and it passes through these holes and then gently creates a film over this plate. Now, this film then is a protective layer and this protective layer then indeed actually physically protects the blade from hot gas that means a layer of cold air is created over the surface of the blade and this cold film creates a protective layer from the hot gas. This can be done by number of method when you have a full blade cooling you have a number of designer holes that are created these are very accurately designed and fabricated very sophisticated manufacturing methods are required to actually create these holes in a turbine blade which as you know are made of high temperature materials and this is a very sophisticated technology. Now, this requires these cold holes to be made very very accurately such that the flow of cold air just comes out and creates a film it does not ooze out like a jet into the actual hot gas of the turbine. So, that is what is required the final method is the transpiration cooling which is a futuristic one not yet indeed deployed with any turbine so far. The entire blade would be made of porous material that means instead of having discrete holes like this the entire blade would be porous and cooling air would come out of it and create a gentle film all over it by providing a cooling layer to the blade surface. This is what the turbine blade cooling does as and when you increase the turbine blade operating temperature you also would need to operate at a higher and higher pressure and as a result of which the relative coolant of the flow actually goes up. So, you need to provide more and more cooling flow if you are operating at higher and higher temperature if you are operating at a higher and higher pressure as it is in normal many of the modern gas turbine engines your coolant flow requirement goes down. So, your coolant flow requirement is decided by the turbine inlet temperature at which you are operating and to some extent it is also decided by the cooling technology whether it is a convection cooling or a combination of filament convection cooling and the futuristic transpiration cooling in which you can see here the coolant flow requirement would actually be much lower all the way from 5 to 40 operating pressure, but such a coolant technology is not yet available as of today and research is going on hopefully to be made available in future. This is a kind of typical turbine blade cooling that is used this is typical turbine blade in the front here you can see the impingement cooling technology which is used to cool the inside of the leading edge which as I mentioned is a hot spot and then you have the film cooling which uses film on the blade surface to create a protective layer over the blade surfaces that is done on both the blade surfaces the upper surface the suction surface and the pressure surface and around this blade you have the hot gas flowing which is continuously heating up the blade. This is often done by flow that flows radially inside the blade you can have very simple cooling which is convection cooling and then you can have some kind of impingement cooling in the inside also this is a combination of convection and impingement the earlier one was a combination of convection impingement and film cooling. This is a typical turbine blade as I mentioned the flow goes radially it comes in typically through the root section of a stator a stator as you know is the first row of blade that faces the hot temperature and that is the one that requires indeed to be cooled first and then of course the cool air goes through the blades radially passes through the blade like this and then a passage is created through which the cold air passes and then finally goes out through some any of the tip. One of the rows of blades over here has holes through which the cold air is impinged on the inside of the leading edge all the way from root to the tip of the blade. So, entire leading edge inside is cooled by impingement cooling from inside by radial cold air flow impinging from inside. So, we have a combination of impingement flow convection flow and then of course these holes which come out creating the film cooling. So, this is typically turbine blade cooling technology that is used in modern HP turbine stator similar, but a little more complicated technology would typically be used in modern rotors cooling is indeed normally provided first to the stator then of course you may need to provide to the rotor also especially in the modern aircraft engines. The technology is a little more complex because you have rotating blades there and you have to be careful in providing your cooling technology which should be operational during the operation of the rotor. The modern LP stage stators are also often cooled and this cooling is necessary because the temperature at the front of the turbine has gone up so much that the LP stages also need some of the LP stages the early LP stages also need some amount of cooling. Quite often the last of the LP stage does not require any cooling it is normally an uncooled blade. Over the last 50 years if you see more and more effort has been given to turbine cooling rather than to turbine aerodynamic design and as the flow in turbine is always in favorable pressure gradient high turbine efficiency is comparatively easily achieved. However, more work done requires more temperature and that is why more effort has been given to raising the temperature the cooling actually reduces the turbine efficiency slightly, but that is a penalty that you pay for getting more and more work out of the turbine. The cooling occurs differentially across the blade surface depending on the local temperature field this is what we discussed earlier and the cooling technology has to be uniquely designed for each and every turbine blade. The amount of cooling may vary from 50 degree as it was in the early years to nearly 500 degree centigrade as in the modern blades. Most of the modern blades also deploy or apply a little bit of coating which is also a blade surface coating to save the blade from high temperature coating is applied in addition to the cooling technology. So, over the lecture today we had looked at various kinds of cooling technology that is deployed in axial flow turbine. These cooling technologies are extremely complex technologies and have been developed over a period of last 50 years and as I mentioned manufacturing turbine blades with these cooling technologies is a very costly affair really each and every blade is hugely costly affair and as a result the turbine axial flow turbine as used in aircraft engine is indeed a very costly product. One of the reasons is employment or deployment of these cooling technologies. We had a look at the axial flow turbine over the last two lectures. In the next lecture we will take a look at radial flow turbines and how the radial flow turbines work. We shall see the radial flow turbines are not cooled they operate in uncooled manner and we will have a look at how the radial flow turbine works, what are its performance parameters and how do they function and what kind of usage they are normally deployed in aircraft engines. This is what we will do in the next class.