 Hello and welcome to lecture number 28 of this lecture series on jet aircraft propulsion. We have been talking about some of the aspects related to one of the components of a jet engine that is the air intake. We have of course, already covered a discussion on other components like compressors and combustion chambers and turbines. And I mentioned in the last class that intakes also form a very important component of the engine. Even though intakes are not really manufactured or fabricated by the engine manufacturer, it is usually manufactured by the airframe manufacturer of course, in consultation with the engine manufacturer. So, in the air intake forms part of the engine when it is installed in an aircraft and not as a standalone unit. And we have also discussed about in the last class about what are the functions of air intake, what are the different types of air intakes which are used. Basically, there are two distinct classes of air intakes one which is used purely for subsonic flows and the other class of intakes which are used for supersonic flows. And we have also seen that there are lots of differences between these types of intakes because of the fact that both these intakes have to operate in different modes or in different regimes of operation. One of them has to operate in supersonic mode in which case the mode of compression is quite different from what it occurs in subsonic flows. And that makes a whole lot of difference between the geometric construction of a subsonic intake as compared to a supersonic intake. We have also seen that in general subsonic intakes are simpler in terms of their design as compared to supersonic intakes. And today we will discuss little more on intakes. We will primarily be discussing about what are the sources of losses or how you can account for performance of these intakes and what are the performance parameters that can be associated with an intake. We will also be discussing in little bit details about some of the issues related to supersonic intakes like what is known as starting problem and what are the critical modes of operation of an external compression intake. So, in today's lecture what we are going to discuss about the following. We will first talk about performance parameters. We will see what are the different parameters that can be used to judge the performance of air intakes. We will then look at where the losses are originating or what are the sources of these losses. We will also be talking about starting problem associated with supersonic intakes. We will spend some time on what is meant by starting problem. And then subsequently we will talk about what are the modes of operation of an external compression intake. So, these are some of the topics that we shall be discussing in today's lecture. And I think in the last class I also mentioned that an intake has to operate over a variety of operating modes that is as an aircraft takes off it is operating at a very low speed. At the same time aircraft requires the maximum thrust during takeoff which means that the mass flow requirement during takeoff is quite high. And after the aircraft has taken off and it has climbed to the required altitude then it is beginning cruise that is when the aircraft does not require maximum thrust at the same time it would have attained its maximum speed. So, the mass flow requirement in these two cases are quite different and also the speeds of operation are quite different. And if it is a fixed geometry intake like what is used in most of the transport civil aircraft the subsonic type of aircraft then which have fixed geometry intakes then unless the intake is very carefully designed under these extreme operating conditions there could be lot of issues with regard to operation and performance of these intakes itself. And so it is necessary that an intake manufacturer or a designer keeps these things in mind. And in the sense that the designer obviously would know the range of operation or the flight regime of a particular aircraft he has to keep in mind the fact that under different operating conditions the engine requirements are quite different. And it is the intake which is going to supply the required mass flow rate not just the quantity, but also of a good quality in terms of a uniform flow into the engine. Because that is very essential for proper operation stable operation of the engine. So, an intake having to operate under these circumstances will have to keep in mind the designer will have to keep in mind the fact that there could be conflicting requirements on what is the operating mode during takeoff as compared to what happens during cruise. So, in a fixed geometry intake there is this problem that you cannot change the geometry, but what do you do if you cannot change the geometry. So, it has to be a trade off between the operating conditions. So, because of the fact that intake operation varies tremendously over operating range for example, during takeoff the engine requires a very high mass flow, but it is operating at a low speed. And so in fixed geometry intake it is likely to have issues with delivering this mass flow during takeoff. And it is the duty of the intake to supply the required mass flow without affecting the engine performance. Let us take one quick look at an example where we see what really happens as the operating conditions change for a fixed geometry subsonic intake. So, here we have a fixed geometry subsonic intake. So, this is how a typical intake would look like for let us say a transport aircraft let us say Boeing 747 7777 and so on. So, all these aircraft are typical subsonic transport aircraft they all have intakes which look like this. And this is the compressor phase of the engine this is the hub of the engine. So, during takeoff as I mentioned the engine is operating at low speed and it requires a high mass flow which means that the stream lines the engine would try to capture stream lines from the free stream from infinity. So, this is our free stream which is been represented as infinity. So, during takeoff the capture area can be extremely hides which is why I have not really shown the capture area here. Capture area refers to the area of the stream tube which actually enters into the engine. And when the engine is just beginning when the aircraft is just beginning to takeoff just when its speed is very low thrust requirement is very high capture area can be extremely high. Now once the engine has taken off and during climb the capture area is still high in fact it is larger than the intake entry area, but it is still definable you can still associate some area with this and that is why we have shown a distinct area for the stream tube and that this is the capture area under this condition which is during climb. During cruise on the other hand you can see that the capture area has reduced substantially it is usually of an area which is lower than the intake entry area as you can see here which means that there will be some amount of deceleration or diffusion taking place even before the flow enters the intake because this is a subsonic flow. And if the engine is accelerating beyond its cruise Mach number then there are possibilities that the capture area becomes even smaller in which case there is a possibility that because it is a fixed geometry intake the adverse pressure gradient here would be quite high for the flow to sustain itself and there could be an occurrence of flow separation on these walls which obviously would lead to poor performance of the engine. And this could happen if it is operating at Mach numbers flight speed slightly more than the design Mach number that is during cruise. So, this is just an example of different modes of operation of a typical subsonic fixed geometry intake. And this is something which all intakes which are operating in this regime will have to undergo that during takeoff it has a certain there are certain requirements for takeoff there are certain requirements for climb cruise and so on. And because geometry is fixed the designer has to ensure by careful optimization that the engine performance is not compromised under any of these operating conditions which means that there could be instances where the intake is not operating is not designed for an optimal operation which is probably during takeoff and climb. But during cruise is when the engine is or the aircraft is going to operate for the longest duration. So, the intake is usually designed to operate most efficiently when the aircraft is cruising. Whereas, during takeoff and climb because those the instances of takeoff or the time period of takeoff climb is much smaller the engine designer the intake designer has to make sure that the engine of the intake operates efficiently though not optimally for that particular operating condition. Now, for a typical subsonic intake like what we have been discussing now there are two modes or two parts of deceleration or compression taking place. One part of the compression is just before the intake that is even if even before the flow enters the intake there in some operating conditions there could be a deceleration and the other part of deceleration is of course within the diffuser or the intake itself. So, there are there is an external compression which is on account of the pre-entry compression as it is called and the other component of this compression is within the diffuser itself. So, these two constituents put together result in the overall diffusion or pressure rise that occurs within as a result of the diffuser, but the pre-entry compression of course is limited to only certain modes of operation like during cruise as we have just seen. During takeoff in fact there could be an acceleration pre-entry acceleration taking place and so there is not that does not really contribute towards the overall pressure rise taking place in the intake and so under these two operating conditions we will now see what really happens within the intake and how we can evaluate what is really happening in terms of pressure rise under these two circumstances that is pre-entry compression and the internal compression. So, compression in subsonic intake consists of two components as I said one is the pre-entry compression or the external compression and second part of the compression is the internal compression or compression within the diffuser. And pre-entry compression is that part of the compression which occurs just before the intake entry itself and because there are no solid surfaces bounding the pre-entry compression pre-entry compression is always isentropic. On the other hand internal compression is occurring within the diffuser surface itself and therefore, internal compression is not always in fact it is never isentropic it is just the pre-entry part of compression which is isentropic which means that it is free from losses isentropic compression is always good because it is free from losses. So, one might wonder then why do you in fact have any internal compression at all why cannot we have the entire compression taking place outside the diffuser itself which means that there are no losses in the diffuser we have 100 percent efficiency for the diffuser well ideally yes one would like to do that but then the very fact that pre-entry compression is a result of the presence of the intake itself that is if you do not have an intake there is no more pre-entry compression. So, intake the diffuser itself is the result or the cause of pre-entry compression and one could definitely try to maximize the fraction of pre-entry compression to the overall compression which is what designers may try to do but in doing so what happens is that pre-entry compression as you have seen is very sensitive to the operating condition that is if the aircraft is taking of or if it is climbing there is no pre-entry compression on the other hand if it is cruising obviously there is a pre-entry compression. So, because of the fact that pre-entry compression is very sensitive to the operating conditions designers not would not want to always try to maximize pre-entry compression and see what they try to do is to get a trade off between the fraction of pre-entry compression to the compression taking place within the diffuser to ensure that there is a proper balance between these two components of diffusion. And the other possibility is that pre-entry compression might sometimes trying to maximize pre-entry compression might sometimes lead to occurrence of flow separation within the diffuser as you have seen in the example I was discussing if the aircraft is let us say operating at a Mach number which is slightly higher than the cruise Mach number than because of the pre-entry compression there could be chances of flow separation within the diffuser surface which is obviously not a good thing for the engine. So, we will now discuss about two different two extreme cases one corresponding to take off where the engine requires high mass flow and the aircraft is operating at a low speed. The other extreme is of course during cruise when it requires lower thrust or lower mass flow, but it is operating at a high speed. So, let us look at thermodynamically what happens under both these operating conditions and we will try to appreciate the fact that pre-entry compression does play a significant role in the overall compression process. So, what I have shown here are two different cases one is corresponding to high speed low mass flow which means take off well which means cruise high speed low mass flow corresponds to cruise. The other extreme is take off which is low speed and high mass flow. Let us look at the cruise condition first. Now, during cruise the engine requires lower mass flow because the thrust requirements are lower at the same time it is operating at a high speed. Now, because it is operating at a high speed the engine as I said is usually designed for this kind of an operating condition where you would prefer to have some amount of pre-entry compression. You can see this is a capture area. Capture area is much smaller than the intake entry area. This is the intake entry area. This is the capture area. Capture area is lower than this which means that because it is a subsonic flow increase in area would lead to diffusion. There is a diffusion taking place from free stream all the way to the intake entry. So, this corresponds to pre-entry compression or pre-entry diffusion and once the flow enters the diffuser geometry because of the very fact that the this is a diffusing geometry in a subsonic flow. There is compression taking place internally also and that is the internal compression. Let us look at this process on a temperature entropy diagram a T s diagram. So, initially the air was at an ambient temperature of T a and a pressure of P a and so this part of compression which is from station a to 1 is the pre-entry compression and that is why you can see that it is a straight line which means that it is isentropic and I had already mentioned that pre-entry compression is always isentropic because there are no losses of friction there are no sources of loss occurring in any of this part right from in a to 1. So, this is isentropic compression from 1 to 2 is diffusion internal diffusion which is non isentropic you can see it is a non isentropic diffusion from 1 to 2. Now, if the whole process were to be isentropic then you would have got a stagnation pressure of P 0 a and because of the fact that there is a certain pressure loss taking place within the internal surface of the diffuser. The pressure that you ultimately get at station 2 is P 0 2 which is less than P 0 a P 0 a corresponds to the isentropic pressure stagnation pressure that you would have got if there were no losses internally P 0 2 is the actual pressure that you get stagnation pressure that you get because of the fact that there are losses frictional losses occurring internally. So, there is a difference between P 0 a and P 0 2 and so we will subsequently define an efficiency which is based on this fact. So, and you can say what is to be kept in mind is that there is no change in stagnation temperature stagnation temperature corresponding to station 2 and station a are the same there is no change in stagnation temperature because stagnation temperature change can occur only if there is heat transfer to the system or from the system. In this case if you assume that these surfaces are adiabatic the flow is adiabatic there is no heat transfer taking place there will not be any change in stagnation temperature although there is still a change in stagnation pressure P 0 2 will be less than P 0 a. Now, let us look at the other extreme operation that is during takeoff it is low speed high mass flow and I mentioned that this intake are usually designed to for operating efficiently during cruise which means that if it is a fixed geometry intake because the mass flow requirement is very high the intake area is fixed and the speed is low. It means that we would the capture area upstream has to be very large because if the engine has to if the intake has to supply that much mass flow rate capture area has to be large because it is this mass flow which will ultimately go into the engine at this speed now during cruise you can see that the speed is very high and therefore, even a smaller capture area would suffice in this case that would not because the speed is low you need a larger capture area to deliver the required mass flow rate. And the problem with both of course, both these operations is that there is some amount of what is known as spillage we will discuss spillage in little detail later on spillage corresponds to that those stream lines which escape and move over the surface of the intake that is known as spillage. If you look at T S diagram for this process the process begins at station A and you can see this area is larger than the intake entry area and because this area is larger there is an acceleration taking place here and there is an acceleration much which is isentropic because there are no losses occurring because there is acceleration there is a drop in static pressure. So, this is P A which corresponds to the ambient static pressure P 1 corresponds to the static pressure at station 1 which is the intake entry. So, there is a drop in static pressure from station A to station 1 and then diffusion takes place from 1 to 2. So, you can see that in this case of course, the again at exit of the diffuser the stagnation pressure is P 0 2 which is less than P 0 A T naught corresponds to the stagnation temperature there is no change in stagnation temperature. Here you can see that the internal compression the fraction of internal compression is larger than what happens here because here P 1 was greater than P A in this case P 1 is lower than P A there is a larger pressure gradient which means that if this area if the design engine or the intake was not designed efficiently under certain cases there could be local flow separation taking place because of the very high pressure gradient that is involved here. So, in these are two distinct modes of operation of a subsonic fixed geometry intake and we have seen that under two extreme conditions the intake operates very differently which is something that one would have expected. And because of the fact that the intake is operating in different modes and the geometry is fixed under off design conditions you can see that the intake operation is quite different from what it is at the design condition. At the design condition the designer would have tried to have some component of pre-entry compression as well. So, that pre-entry compression which is isentropic and loss free also leads to some amount of overall pressure rise whereas under off design conditions like during take off for example, pre-entry compression does not exist and in fact there is an acceleration taking place pre-entry and therefore that increases the pressure rise that has to take place internally and that is where the optimization of the intake comes into picture that the designer needs to make sure that even even though the pressure rise that the internal compression has to take give does not lead to substantial pressure gradients which might lead to flow separation. So, which brings us to the fact that there are certain operating conditions under which intake might operate sub optimally and there could be flow problems associated with operation of such an intake. So, let us take a look at what are the possible regions of flow problems which typical fixed geometry subsonic intake might encounter. So, there are three possible locations for flow separation in typical subsonic fixed geometry intake. One is of course, external to the intake that is on the nacelle the other the other two locations are within the internal part of the diffuser itself. One is within the internal diffuser internal surface other possible location is on the center body of the hub. Now, if we have flow separation on the nacelle which is possibly a recent result of spillage which occurs on the intake spillage might lead to flow separation on the nacelle under certain conditions. This can increase the overall drag of the aircraft and separation within the diffuser geometry obviously, may lead to higher stagnation pressure laws and therefore, lower diffuser efficiency we are going to define diffuser efficiency shortly. So, pressure flow separation can lead to higher pressure losses which means lower diffuser efficiency. So, these are this is just an illustration of where these flow problems might occur. This is the leading edge of the intake which is the lip of the cowl and the this is the external surface of the nacelle and one of the sources of or possible locations of flow separation is on the external surface which might occur if there is a large difference between the capture area and the intake entry area under which conditions there could be a substantial amount of spillage and spillage under extreme operating conditions might lead to flow separation from the external surface which obviously, increases the overall drag of the aircraft. The other two locations are one is on the internal surface I mentioned that during takeoff for example, the capture area is very high very large and there is a pre entry acceleration taking place leading to a drop in static pressure at the intake entry which means that there is the amount of pressure rise that the internal surface of the diffuser has to take place is much larger which might in some cases lead to flow separation from the internal surface and under certain conditions flow might separate from the centre body or the hub of the engine as well. In fact, both these sources of separation which are internal to the diffuser affects the diffuser performance in terms of its efficiency and pressure stagnation pressure ratio. Separation external to the surface does not really affect the diffuser performance, but if it affects the aircraft performance as a whole bit because it increases the drag. So, these are possible locations of flow separation which might affect the performance of the intake two of them obviously, affect the intake directly the external separation on the nacelle affects the aircraft performance as a whole. Now, we have seen that there is some stream lines which do not form part of the capture stream tube or the capture area and under some operating conditions these stream lines escape and move over the surface of the nacelle. These stream lines are basically referred on the mass flow associated with this is referred to as spillage. Now, spillage is under certain operating conditions under off design conditions may lead to increased external losses that is external drag. And so, spillage is something which occurs under two conditions one is if the capture area is larger than the intake entry area or even if the capture area is smaller than the intake entry area which means that spillage will occur will not occur only if the capture area is equal to the intake entry area. So, spillage always occurs when the incoming stream tube or the capture area is different from that of the intake entry area presence of spillage will lead to increased drag and under certain conditions may also lead to flow separation on the cowl or on the nacelle. Now, a designer would like to maximize external deceleration or pre-entry compression because it is devoid of any losses and, but the problem with this is that one first problem is that it is very sensitive to the operating condition. And the other issue is that external deceleration may also cause the occurrence of spillage which increases the overall performance of the aircraft. So, which means that the designer has to carry out a trade off between internal and external deceleration depending upon the design condition of the intake which is usually during cruise of the intake of the aircraft which is when aircraft operates for the maximum duration. And so, trying to have larger amounts of pre-entry compression could lead to spillage on one hand and on the other hand it may also lead to issues with the internal diffusion itself under other operating conditions like flow separation within the diffuser. And therefore, it is always a trade off between how much amount of pre-entry compression we can have as compared to the overall compression of the intake itself. We will now quickly look at how we can having understood the different modes of operation of subsonic intakes. We will now look at how we can evaluate the performance of intake and what are the performance parameters which we can associate with an air intake. We have already discussed about one of these parameters in some of our earlier lectures during cycle analysis and that was the isentropic efficiency. So, efficiency or isentropic efficiency is one of the parameters using which one can evaluate the performance of intakes, but there are other parameters as well like pressure ratio and distortion. So, let us take a quick look at some of these performance parameters and these performance parameters are valid for both subsonic as well as supersonic intakes. The three parameters which are normally used one is the isentropic efficiency which we have discussed we will also discuss that quickly in today's class. Then there is stagnation pressure ratio or sometimes referred to as pressure recovery and then there is a distortion coefficient. So, isentropic efficiency we have already discussed this in the earlier class in some of our earlier lectures refers to the difference in stagnation pressures leading to or the efficiency is basically defined in terms of the temperatures that corresponding that correspond to the difference in stagnation pressures as a result of loss in stagnation pressure within the diffuser. So, you can see that p 0 2 and p 0 a are two pressure lines stagnation pressure lines p 0 2 corresponds to the actual pressure stagnation pressure p 0 a corresponds to the ideal stagnation pressure both of them fall on the same stagnation temperature line. There is no change in stagnation temperature, but there is a change in this stagnation pressure. So, we are going to define efficiency based on these stagnation temperatures which correspond to a process which would have been isentropic. So, the efficiency of a diffuser is defined as h 0 2 s minus h a divided by h 0 a minus h a. So, h 0 2 s corresponds to this point on p 0 2 which is the actual stagnation pressure and h 0 a corresponds to the ideal stagnation enthalpy which is falling on the ideal stagnation pressure line. So, this simplifies to t 0 2 s minus t a divided by t 0 a minus t a. So, this is how we have we define isentropic efficiency of a diffuser which is defined in terms of temperatures, but it is not because of loss in stagnation temperature, but it is because of loss in stagnation pressure. The other parameter is the stagnation pressure ratio or pressure recovery which is simply the ratio of the outlet stagnation pressure to the inlet stagnation pressure p 0 2 by p 0 a. So, we can relate these two stagnation efficient isentropic efficiency and stagnation pressure ratio and. So, if you simplify I think we have carried out this exercise earlier the diffuser efficiency would be a function of the Mach number and the stagnation pressure ratio. So, if diffuser efficiency would be 1 plus gamma minus 1 by 2 m square multiplied by pi d which is stagnation pressure ratio raised to gamma minus 1 by gamma minus 1 divided by gamma minus 1 by 2 m square. The other performance parameter which is used is known as the distortion coefficient which is a measure of the intake exit flow non uniformity. Because we have discussed that the flow exiting the compressor exiting the intake has to be uniform non uniformities in the intake exit flow will drastically affect the compressor performance and therefore, the engine performance as a whole. So, how do we measure or quantify this non uniformity. There are different definitions for distortion coefficient one of the most commonly used definition is known as d c subscript theta where d c stands for distortion coefficient d c theta is usually defined as the difference between the average stagnation pressure at the exit of the diffuser minus the average stagnation pressure in a sector theta where the stagnation pressure is minimum divided by half rho v infinity square. So, p 0 2 average is the average to stagnation temperature stagnation pressure at the outlet of the diffuser. So, if we take an average let us say this is the diffuser outlet cross section we take an average of the stagnation pressure over this entire cross section that is p 0 2 bar p 0 2 theta minimum is the average stagnation pressure in a sector where this stagnation pressure is minimum. So, we define a sector theta and measure stagnation pressure in that average stagnation pressure in that scan the sector over the entire circumference and for that sector where the average stagnation pressure is minimum is what is used here this divided by the inlet dynamic pressure gives us d c theta. So, in this case theta I have shown here corresponds to that sector where the average stagnation pressure is minimum. So, which means that we will have to take this scan this entire circumference for sectors theta where the pressure is minimum. So, based on this we can have different ways of defining d c theta depending upon the sector angle chosen and one of the most common angles used is sector angle 60 degrees and that is why d c this distortion coefficient for that is known as d c 60 where 60 corresponds to the sector angle. There are other angles which are also used sometimes 45 degrees and 90 degrees in which case it would be d c 45 and d c 90, but d c 60 happens to be or has been proven to be the most common way of defining distortion coefficient and it is widely used by the engine manufacturers all over. So, an engine when it is supplied comes with these parameters well the intake comes with these parameters one is the pressure recovery which is related to the thrust because lower the pressure recovery obviously it will affect the thrust correspondingly d c 60 tells us what is the amount of distortion that the intake will deliver and every engine will have a certain level or limit of d c sensitivity beyond which the engine operation might get affected. So, the intake designer has to keep these parameters in mind while designing the intake. So, we now move on to supersonic intakes we have discussed about subsonic intakes so far of course, all the performance parameters I am discussed just now is valid also for supersonic intakes. Let us look at some of the issues related to supersonic intake operation like what is meant by starting and what are critical modes of operation of intakes and so on. Now, during our last lecture we have I mentioned about three types of intakes internal compression external compression and mixed compression intake that is one way of classifying supersonic intakes. So, we will discuss our discussion in today's lecture will be based on this classification of intakes. So, internal compression basically involves internal compression intake involves compression which is taking place entirely within the diffuser geometry itself and that is the shocks that eventually lead to deceleration would occur within the surface of the intake itself external compression involves shocks which are outside the geometry of the intake mixed compression is a combination of these two. And so depending upon the type of intake the flow problems associated with that are also slightly different, but one of the problems is usually present in all the three that is basically known as starting of an intake we will discuss that in little bit detail. So, internal external and mixed compression intakes let us look at typical geometries of these types of intakes. This is an internal compression intake you can see all the shocks structure and shock system is within the intake itself or several oblique shocks eventually ending in a normal shock where which is basically the throat of the intake. In an external compression intake we have oblique shocks ending in a normal shock all of them are outside the intake itself of course, the ramp is still outside ramp is the one which leads to formation of these shocks and this is the normal shock. In this case there are two oblique shocks and a normal shock mixed compression intake involves part of the compression which is external this is the external compression and part of the compression which is internal this part of the compression takes place internally. Now, in supersonic intakes as we have seen are characterized by presence of shock and but these intakes have to operate right from very low subsonic speeds all the way to supersonic speeds and which means that we will have to establish a shock system as the intake approaches supersonic or as the intake reaches supersonic speeds and this is often a bit of a problem trying to establish a stable shock structure. And so, this process by which one would establish a stable shock structure for stable operation or steady operation of the engine is known as starting of the intake that is one would need to always start an intake where in one establish a stable shock structure which leads to which results in minimum pressure loss and that is in some types of intakes it is a big challenge to establish a stable shock structure. So, we will discuss about one of the geometries where this problem is more pronounced that is in an internal compression intake which involves shocks within the diffuser geometry itself. And we will discuss about one such geometry and this process by which the shock structure is established is known as starting of an intake. So, let us look at starting problem of an intake. Now, this is an internal compression intake and so, as the engine begins its operation from very low subsonic. So, you can see Mach number is less than 1 and it continues to remain less than 1 the intake has just started this a corresponds to the capture area this is the intake entry area and this is the throat area. Now, as the engine accelerates at a certain Mach number which is still subsonic free stream Mach number is still subsonic the flow might reach sonic speeds at the throat, but continue to remain subsonic even downstream of that because the back pressure is not low enough. As we accelerated further as the engine approaches sonic speeds as the flight Mach number approaches sonic speeds there could be an occurrence of a weak shock because Mach number has now reached 1. There is a weak shock which is ahead of the intake itself downstream of the shock Mach number is subsonic because it is subsonic in this section because which is converging the flow accelerates and it might reach sonic speeds at the throat and continues to remain subsonic downstream. The presence of this weak shock also means there would be downstream of the shock it is subsonic, but before that it is supersonic or sonic and so, the stream lines are straight because in a sonic or supersonic flow the information does not travel upstream and therefore, all these stream lines upstream are straight. After the weak shock the flow gets diverted and that leads to spillage occurring at this particular Mach number. Now, as we increase the Mach number further at supersonic speeds this weak shock becomes a strong shock and it takes a curvature and this is known as a bow shock and downstream of the shock it is a subsonic Mach number Mach number becomes sonic at the throat and then it continues to remain subsonic. What might think? Why not operate the intake in this condition? There are two problems of operating an intake under this condition. One is the fact that there is a strong shock leading or ahead of the intake which means the stagnation pressure losses are substantial. The other problem is that there is substantial spillage taking place leading to external drag as well. So, one would not want to operate the intake with a strong shock ahead of the intake. So, if let us say we change the Mach number from its supersonic Mach number, we increase the Mach number or decrease the Mach number. Let us say we have a Mach number which is which is a design Mach number which is slightly less than the design Mach number in which case the shock will now get attached to the leading edge of the intake. So, this shock is now attached right here at the leading edge downstream of that the flow is subsonic it reaches sonic speeds at the throat and then subsonic again. This is again not desirable because the pressure losses here the spillage is minimal. There is no spillage here because you can see the capture area is exactly equal to the intake entry area. So, there is no spillage, but the stagnation pressure losses still persist in this case. So, if we were to accelerate it further from the design Mach number to a slightly higher Mach number then we can have a shock which will move into the intake now. The shock system is a normal shock is never stable in a convergent section, but it can operate or it can attain a stable position in a divergent section. So, we now have supersonic Mach number all the way here up to the normal shock which is in the divergent section and then subs downstream of that we have a subsonic Mach number. And after this if we decelerate and bring the engine back to its design Mach number we then have a now this same normal shock which moves slightly upstream and attains a stable position just after the throat. So, just around the throat we have a normal shock which is very weak it is weak because of the fact that it is very near the throat where the Mach number reaches unity. And therefore, because it is a weak shock there is the pressure losses across the shock is minimal. The other advantage is that because it is supersonic all the way up to the throat there is no spillage because the capture area and the intake entry area are the same. So, as the Mach number reaches its design Mach number we have a weak shock here right after the throat subsequent to that we have a subsonic flow. So, this is the condition ideal condition that one would like to have before the intake is said to have been started. So, when we say that the intake has been started we mean that there is a normal shock which is operating or which has attained a stable position right after the throat. And it is to kept right after the throat because that is where the Mach number is minimal. So, the pressure losses across the normal shock is minimal and under this operating condition there is no spillage also under this condition. So, this is the starting problem. So, which means that though I have explained it in simple terms in an actual engine it is not that simple to establish a stable shock system by either accelerating beyond the design Mach number or and so on. There are other ways of implementing this by changing the throat area and so on. I have not discussed that here, but in simple terms establishing a stable shock structure right after the throat is very essential for efficient operation of the engine because that is when you have lower minimal total pressure loss without any spillage. And this is a problem which is more severe in these types of intakes which are pitotipe internal compression intakes. They may also be present in some of the external compression or mix compression intakes, but they are not as severe as what we have discussed for this case. So, we will now discuss about external compression intakes and associated problems with that. In external compression intakes the compression takes place outside the covered portion of the intakes and you usually have one or more oblique shocks followed by a normal shock. And depending upon the location of these shocks the intake may operate in subcritical mode, critical mode of the design mode or supercritical modes of operation. Subcritical mode is when Mach number at Mach numbers below design value the normal shock and the oblique shocks are placed well ahead of the cowl lip. There is a high external drag due to spillage under this operation. In supercritical mode of operation which occurs at the same mass flow as critical mode higher losses occur because the normal shock will occur in a region of higher Mach number. I will explain this in the next slide. Critical mode is a design mode of operation. Normal shock is located exactly at the cowl lip. So, these are the three modes of operation. Subcritical mode the oblique shock and the normal shock are ahead of the cowl. Therefore, there is spillage and losses associated with that. Supercritical mode is when the normal shock has now moved downstream of the throat which means that the flow is supersonic here all the way up to normal shock. And therefore, in a supersonic flow a divergent well this is a convergent section here in this case leads to acceleration of the flow which means that the Mach number keeps increasing from the intake entry all the way up to the normal shock. So, the normal shock is now occurring in a Mach number which is higher than much higher than Mach 1. Therefore, stagnation pressure loss is higher in supercritical mode. Critical mode is when the normal shock occurs exactly at the cowl lip here and therefore, and that is the throat. Therefore, the losses across this normal shock will be minimal. So, this is how the this is the operating condition for which the intake would have been designed for. So, that normal shock occurs right at the cowl lip. Now, operation of this type of intake is also tricky, but usually the position of the ramp is adjustable it will not be a fixed ramp it would be adjustable. And depending upon the mode of operation of the engine the ramp position is adjust. So, that adjusted so that the normal shock can be fixed at the cowl lip itself and that is where it operates under critical mode of operation. So, total pressure losses will be highest in the case as we have discussed in the case of a diffuser which has just one normal shock ahead of it. We have discussed that when we are talking about starting of an intake if we had a strong oblique shock right ahead of the intake entry total pressure losses would be very high. Because the we have a shock a strong shock which is in ahead of the intake total pressure losses are high which means that a better option would be to have multiple shocks multiple oblique shocks eventually having ending up in a normal shock. So, that before the flow enters or hits the normal shock it is Mach number is low enough. So, that losses across the normal shock is minimized. So, instead of decelerating the entire supersonic flow to subsonic through one normal shock it is a normal practice to use multiple oblique shocks eventually ending in a normal shock. So, that losses can be minimized and this is usually achieved using ramps. I have shown one example where we had a ramp with two steps resulting in two oblique shocks and then one normal shock. So, if we increase this infinitely if you have infinite number of normal oblique shocks and then a normal shock then the losses can in this case set to be 0. This is possible if we have a contoured ramp which will result in generation of infinite number of oblique shocks which are very very weak and then a normal shock and. So, in this case the flow can be said to be isentropic if you of course, assume that frictional losses are minimal and such a diffuser is known as an isentropic external diffuser where there are infinite number of oblique shocks and then a normal shock the losses across the shocks are minimal. So, oblique shocks in a diffuser which has a very smoothly contoured center body may have infinite number of oblique shocks and that is known as an isentropic external diffuser. So, this is just an illustration of an isentropic external diffuser. If we ever if we are able to contour this center body in such a way that we have infinite oblique shocks which are weak and then a weak normal shock then a supersonic flow can be decelerated through all these infinite shocks eventually to subsonic Mach number through these shock infinite shock system. Now, though theoretically this is very much possible such a diffuser would be extremely sensitive to the location of the ramp itself that is any small change in the operating condition would require a corresponding change in the ramp location which means which is physically not feasible to implement and that is why we do not really have such an intake operational and so because it is extremely sensitive to the operating condition theoretically it is still possible to have an intake which has a shock system and it is still close to isentropic diffusion taking place through these shocks. So, in today's lecture I am trying to wind up today's lecture and we will just look at what we have discussed in today's class we started our discussion with subsonic intakes we talked about subsonic intakes and how we can evaluate performance of subsonic intakes. We have discussed about different modes of operation of subsonic intakes especially what happens under extreme operating conditions like takeoff or cruise. Discussed performance parameters which are valid for both subsonic and supersonic intakes and the sources of losses in these intakes. We have discussed in brief about starting problem in supersonic intakes and we also discussed about different modes of operation of an external compression intakes. So, these are some of the topics that we had taken up for discussion in today's class and that will bring us to the end of this chapter on intakes. So, last to this lecture and the previous one we had discussed about intakes their operation different types of intakes and problems associated with intake operation and so on. In the next lecture we will discuss about yet another important component of an engine which is the last component of an engine the intakes constitute the first component of an engine diffuser well nozzles from the last component of an engine. So, in the next lecture we shall be discussing about nozzles. We will discuss about different types of nozzles fixed and variable nozzles and in a similar manner as we discussed for diffusers we will discuss about types of nozzles. We will also discuss about problems associated with some of these nozzle operation. So, this we shall take up in the next lecture when we shall start discussing about nozzles and different types of nozzles.