 Now, you have done chapter on cycle analysis of jet engines. Today, we will extend that jet engine coverage to working of ramjets and pulsejets, in which the basic cycle understanding that you have acquired for jet engines would be useful. We will of course, also look at the cycles of ramjets and pulsejets, which are similar to the cycles that you have done. So, that would be quite easy for you to extend your understanding. The ramjets and pulsejets actually historically precede those of the turbojet engines. They had actually been used for flying aircraft during the world war II. And as a result of it, understanding of how ramjets and pulsejets actually work had been created quite some time back. However, the advent of turbojets and various kinds of turbofans actually put the ramjets and pulsejets in some kind of a back burner. Over the years, of course, people realize that they have their utility specially the ramjets and the modern version of ramjets known as cramjets, which are used for high speed aircraft typically supersonic or even hypersonic aircraft, where actually you cannot use the turbojets. The turbojets they have their utility value from subsonic to supersonic up to may be about Mach 3. And then beyond that, you need different kind of engines or thrusters to create thrust for aircraft or flying vehicles, flying at those kind of Mach numbers. So, the ramjets and scramjets have been revived and various versions of them are now under development in various countries all over the world. And some of these fundamental issues of these ramjets and a look at what is a scramjet and of course, a look at what is a pulsejet we will be doing in today's class. Now, ramjets and pulsejets are very simple devices really. They actually involve jet engine without compressors and turbines. However, if you have done the cycles of jet engines, you know that there is a process of compression. There is a process of expansion, which is often done through turbine and in jet engines the turbojet engines the turbines exist essentially for running the compressor. So, if you do not have a compressor, you do not need a turbine. And if you can get rid of the turbine and the compressor, you have a very simple engine configuration a very simple jet engine and that is exactly what a ramjet actually is. So, ramjet is a jet engine without compressor turbine. There are no shafts, no rotating parts and as a result it is a very simple jet engine device for making thrust and have been used as I said for flying aircraft earlier and now they are flying aircraft, missiles and other vehicles. Because of the simplicity of the ramjet configuration, various versions of the ramjet have actually now been conceived. Some of them are still being developed, some of them are still on design board, some of them are being considered along with you know various other kinds of engines including turbojet engines and as a result of which ramjets and scramjets various versions of them are now under development and a few of them under usage in various aircraft and other flying vehicles. Let us take a look at what these ramjets are and how do they function. If you look at the ramjet schematic, you would see that there is a flow coming from the intake side which is at Mach number normally greater than 1. Quite often the modern usages Mach number would be pretty close to 5 or even higher. Some of the ramjets or scramjets being used would be at flying Mach number of the order of 8, 9 or 10. Now, if you have that kind of a Mach number at the entry or the flight Mach number, the flow at the entry is of that Mach number, you require a kind of an intake configuration that has capability to handle shocks because the moment you put a solid body in a high flight Mach number is going to create shocks. So, you need to create a situation over here whereby the shocks are generated and it is necessary that they are designed shocks. So, these shocks are actually designed to operate or be positioned in the intake system of the ramjets and the flow comes in through these shocks and they get supersonically decelerated or diffused or compressed. So, first what we have is supersonic compression through the intake system, through a series of shocks, most of these are all of these are actually to begin with oblique shocks, ending finally with a normal shock at the end of which the flow actually does become subsonic and then you have subsonic diffusion through a normal diffusion process. So, you have a supersonic compression followed by a subsonic diffusion or subsonic compression and then a vastly decelerated flow and huge amount of kinetic energy with which it is coming in is now converted to pressure and this high static pressure air is now fed into the combustion zone. Now, there is no compressor, so the entire compression is done by the supersonic and subsonic compression. And after this aerodynamic compression process, the flow is delivered on to the combustion zone where you have normal what you see here are the flame holders and then you have a normal combustion phenomenon at low subsonic speeds, you require low subsonic speeds to have a good efficient combustion and once the combustion process is over the flow is allowed to mix up. So, you have a uniform flow profile of temperature, pressure etcetera and energy level and then that is allowed to be delivered or fed into the nozzle which is quite often a convergent divergent nozzle and then this convergent divergent nozzle then exhaust the gas high temperature gas into the atmosphere back again. So, thereby creating a exit jet. So, our intention of this jet engine is to create a exit jet of a higher velocity than what it came in with and as a result of which there is a overall momentum increase across the jet engine for the amount of mass that has come in with a little bit of fuel addition and this change in momentum created by the jet engine of course, creates the thrust and this thrust would then enable the aircraft to fly. So, the whole engine essentially is there to create a momentum change across the jet engine thereby creating a forward thrust. So, as you see we have simple elements over here, we have an intake which has to be properly designed to handle the shocks and keep the shock losses to the minimum and then we have flame hondles where you have the combustion. We need a very good efficient combustion and what you see here of course, is annular combustion chamber and then normally you would have a C D nozzle. One of the reasons is the huge kinetic energy which has been converted to pressure as I mentioned the Mach number quite often here is of the order of 4 or 5 and as a result of which the pressure generated here is of a very high order and hence it is quite suitable for use for C D nozzle. C D nozzle as you know is used normally when ideally pressure ratio available that is total to static pressure ratio available is of the order of at least 2. So, normally you would use it only when the pressure ratio is of the order of 4 or 5 and that is the kind of pressure which is normally generated and as a result of which this C D nozzle now creates supersonic exhaust jet. This exhaust jet then has a velocity which is higher one of the reasons is we have added energy we have burnt fuel and added energy to the air and this air now has extra energy with which it can go out with the high velocity and then this high velocity then of course, creates the overall momentum enhancement or increase that creates the thrust. So, you see this is a very simple device which can create thrust without needing any compressor or turbine. However, you do see that you have a compression process you have a combustion process and you have an expansion process through the C D nozzle. So, the thermodynamic processes that you have done earlier in earlier lectures are still there and hence you know we will see that it still follows the so called joule Brayton cycle. So, this is how a ramjet normally would be operative during its operation. If we look at what are the key features of a typical ramjet engine firstly it produces power by increasing the momentum of the working fluid which in our case is air the atmospheric air that is available. Now, in contrast to the air breathing engines that we have worked with before the working cycle is performing without any compressor or turbine and it also does not need an enclosed combustion which is often used in turbojet or turbofan engines where the combustion is isolated for very high efficiency. However, in ramjet engine such an enclosed combustion is dispensed with and you have a overall annular combustion chamber with flame holders distributed all over the combustion zone. And hence as a result of this the ramjet is mechanically one of the least complicated jet engines for thrust production and this is very useful for flying vehicles. Now, ramjet can apply compression to the air by ram compression and as we have seen the compression it does is aerodynamic compression or simply called ram compression part of it is supersonic part of it is subsonic. And this of course has one issue since the compression is dependent on the ram compression or aerodynamic compression it is entirely dependent on the entry mark number. Now, mark number above 2 creates reasonable amount of ram compression, but as the entry mark number starts going down the amount of compression that would be available aerodynamically becomes less and less and less. And as a result of which a ramjet is actually very useful in supersonic speeds, but at very low speeds and specially during takeoff and landing it actually cannot deliver much of compression. And if it cannot deliver compression it cannot really effectively work as a good jet engine. So ramjets utility is restricted to supersonic speeds it cannot really be used for takeoff and landing of an aircraft. Now, this is one of the problems of ramjet and we shall see that because of this the ramjet usage is somewhat restricted. At very high mark number as we have seen the shocks of the intake are present and these shocks of course produce a large amount of losses. These are aerodynamic losses which manifest themselves in the form of pressure losses. Now, these pressure losses of course finally tell on the ramjet performance. So, some of these are the features the fuel that is injected into the stream is after the diffusion of the flow through the intake system through supersonic and subsonic compression and when once the air has been sufficiently compressed and sufficiently diffused to low velocity the fuel is injected. And as a result of which we get a high temperature, high pressure gas available from the combustion chamber and this gas is what is then released through the nozzle. Now, this nozzle is normally then a convergent divergent nozzle of course you can have only a convergent nozzle with the flow going sonic at the exit phase which is which would be the throat that is possible, but that will have a very little utility value. The real utility value is of nozzle which are indeed convergent divergent and would normally be used for most of the ramjet application that we know of today. Now, it is assumed to begin with that the exit pressure P e is pretty close to if not exactly same as the ambient pressure and as a result of which the flow which goes choking at the throat it has to be higher than the ambient pressure. So, P c the throat choking pressure at the throat is always higher than the ambient pressure which is at the exit pretty close to the exit pressure P e. So, let us take a look at how the ramjet compare with the other jet engines. As you can see here the graph has been plotted with reference to Mach number and specific impulse which is actually thrust per unit weight of flow and normally in most of the rockets and other flying vehicles at high altitudes and space the specific thrust is often designated as specific impulse that is thrust per unit weight of flow of fuel and whatever other oxidizer are there. Now, in case ramjets and turbojets the other oxidizer is only air. So, the ISP would be designated accordingly. Now, what we see here is a comparison between turbojets ramjets and scramjets. The blue ones over here are once we using the normal hydrocarbon fuels the air turbine fuels that we know of and these create the ISP configuration as we see they are reasonably good ISP configurations at very low Mach numbers. Now, as the Mach number starts going up the typically the turbojets at Mach number about 3 or 2.5 or 3 turbojets become less and less competitive and ramjets become more and more competitive and then up to a Mach number about 7 or 8 ramjets are very good and then from there onwards you have the scramjets which actually are the better efficient fuel efficient engines. So, typically if you have a cruise which is going on say around Mach 8 at this range you have a choice between ramjets and scramjets and typically turbojets are out of contention and as a result of which many of the vehicles that are being planned for various applications today including space travel are built around ramjets and scramjets. Rockets of course, come into use for even higher Mach number and they have a much lower ISP, but as you can see at very high Mach numbers where the rockets fly to space rockets actually are the more useful vehicles at very high Mach numbers above 10 the vehicles using ramjets scramjets are still being designed we still have them do not have them flying as yet. So, we have flying vehicles which are around Mach 8 some of them are for military applications and a few of them are being thought of for various kinds of space travels and other applications. So, the other thing which you see in the diagram is that it shows two kinds of fuel one is the hydrocarbon fuel which is in blue the red one is actually hydrogen fuel where hydrogen is used as fuel and oxygen of course, is either taken from air in case of rockets of course, both hydrogen and oxygen would be actually carried by the rocket body in terms of liquid hydrogen and liquid oxygen. However, in case of ramjets and of course, futuristically in terms of other jet engines if we use hydrogen fuel you can see for example, the value of ISP would be of a much higher order than the hydrocarbon fuels and. So, if you use hydrogen as fuel you do get higher ISP of all the jet engines turbojets ramjets and scramjets going all the way to rockets at very high very very high Mach numbers. The problem with hydrogen fuel is it is being used already in rockets as I said. However, the problem essentially is that it is a lighter fuel and as a result of which you need more space to carry it with you on any aircraft. So, the space required will be more than a normal hydrocarbon fuel even though hydrogen actually gives higher ISP and it is also a much cleaner fuel in terms of environmental and pollution effects. However, that is in future and it is possible in future more and more jet engines would actually be flying with hydrogen as fuel. At the moment most of them are still flying with hydrocarbon fuels or fossil fuels as we know them. Now, we shall look at the ramjet cycle. Now, cycle you have done you have done the various kinds of jet engine cycles. You have done the Brayton cycle or the Joule Brayton cycle as it is known and you know that it operates on constant pressure combustion phenomenon. Now, that is that cycle concept that you have already gathered would be now extended to analyzing the ramjet applications and we shall see that the cycle that you have been familiar with now work more or less the same way. So, if we look at the ramjet cycle you see that we again have an open cycle. So, the return path from 4 to 1 is open and the ideal cycle is the dotted cycle which you know operates from 1 to 0 to prime and then from 0 to prime to 0 3 prime and then down to 4 prime. Now, that gives you the ideal ramjet cycle which is what I believe you have already done in some detail and you know how to calculate a Brayton cycle performance. You could actually use the same cycle knowledge to analyze the ramjet cycle also. The real cycle of a ramjet is slightly different. The path from 1 to 2 is not isentropic. So, it does not go up straight it goes up with a slight increase in entropy. So, there is a certain amount of efficiency that comes into the picture which we shall normally be calling isentropic efficiency of the compression process. And then in the combustion process there is likely to be certain amount of pressure loss most of which is a fluid mechanic pressure loss. So, that pressure loss needs to be accounted between 0 2 and 0 3. So, the 0 2 and 0 3 are on two different pressure lines ideally as we know from 0 2 prime to 0 3 prime it is supposed to be a constant pressure combustion. However, actual combustion is not exactly constant pressure there is a small amount of pressure loss which is mainly fluid mechanic pressure loss. And the combustion efficiency as you know is typically of a very high order in constant pressure combustion. So, we will continue to treat it as more or less constant pressure combustion and then you have the expansion process there is no turbine. So, you have fully expansion in the nozzle and this expansion process is again not isentropic unlike from 0 3 to 4 it is non isentropic process or a polytropic process and as a result there is a slight increase in the entropy. So, there is a total increase in entropy from 1 into the other and as a result of which the whole cycle will have certain efficiency which again you are familiar with. Now, at the entry to the jet engine you have certain amount of kinetic energy which is shown over here. Now, this kinetic energy is what the flow is coming in with due to the flight and this is the kinetic energy which gets converted to pressure. At the face of the combustion chamber it has a much smaller kinetic energy. So, the idea of diffusion is to create compression and bring down the kinetic energy from very very high values to somewhat low values which are friendly or convenient for combustion purpose. As you might be knowing combustion at very high speeds is a big problem it is something which needs to be taken care of separately. So, normal combustion is done in constant pressure flowing fluid combustion in jet engines is normally done at somewhat low subsonic speeds. So, we got to bring the flow down to that low subsonic speed and from there the combustion take place it takes the whole air fuel mixture to very high temperature from T 0 2 to T 0 3 along this constant pressure line. So, now we have high pressure and high temperature and the gas is then released from that 0 3 position through the nozzle and when it comes out it comes out with a jet of a velocity of the order of C 4 and this has to be higher than the velocity with which it came in. So, typically C 4 needs to be higher than C 1 with which it came in only then you get a positive thrust. So, the idea of this jet engine is of course, to create a value of C 4 exit kinetic energy which is definitely higher than the inlet kinetic energy and then you have a good chance you have assured of a positive thrust. So, this is how the cycle of a ramjet engine which you just had the look at the schematic and the cycle operates along these joule Brayton cycle which you are familiar with. Now, let us look at how this cycle can be converted to our understanding of how the ramjet actually performs. One of the things is it operates on joule Brayton cycle. The next thing is that each of the legs of the thermodynamic cycle has certain irreversibilities. Thermodynamically you have learnt what the reversible and irreversible processes are and in this cycle actual cycle or a real cycle the legs are actually irreversible and as a result of which there are certain pressure losses which are accompanied by each of these processes that is compression, combustion and expansion and as a result of which large amount of pressure loss actually takes place. And as shown in the diagram the diffusion process is a diabetic, but irreversible and as a result large amount of total pressure losses take place. The heat addition in the combustion chamber is accompanied by again pressure loss. So, you have pressure loss at every step of the jet engine operation and all these pressure losses when they are put together you have a situation that the pressure that is available at the entry to the nozzle is somewhat less than the ideal pressure which one would expect in a ideal engine and hence the flow through the nozzle would be somewhat less than the ideal engine flow and the velocity that you would get at the exhaust would be less than the ideal velocity and this is what a real cycle analysis would actually show that the exit velocity would be somewhat less than the ideal and if one is not careful in the design the exhaust velocity could be substantially lower than the ideal engine in which case you have to first ensure that you have a ramjet engine that is providing you with positive thrust because it is entirely possible that during certain operating point the ramjet engine may not reduce positive thrust it may start producing negative thrust because the losses inside the engine could be very high and the exhaust nozzle is not able to produce sufficient momentum enhancement through the nozzle and then the engine would fail to produce positive thrust. So, this is something which needs to be very carefully estimated before the ramjet engine design is finalized. Of course, certain amount of additional losses do occur inside the exit nozzle which has supersonic flow and as a result of which certain amount of losses through supersonic fans and shocks can also take place in addition to the friction losses through the surface of the nozzles. Now, if we write down some of the understanding that we have gathered about how the ramjet engine actually performs we can write down the thrust of the engine which we say as F which is a thrust force in terms of rho V A into A 1 which is of course, the mass flow which is coming through the intake of the engine. So, that essentially is the mass flow and then m bar which we are defining here and into V e minus V a and this is the momentum thrust. So, this whole first term is the momentum thrust and then you have the pressure thrust which is A e into P a and that into P e by P a minus 1. So, we have to ensure that P e by P a is either one or more than one if this is less than one this second term is going to give you negative contribution and we certainly do not want that. So, P e needs to be at least equal to one or more than one as we know if P e is exactly equal to P a this component becomes 0, but V e is maximized. So, maximum V e is actually when P e is equal to P a and hence you get maximum V e and then you get maximum momentum thrust and indeed that is the maximum thrust that this engine can generate when actually P is equal to P a. So, 0 pressure thrust does actually mean maximum momentum thrust and indeed maximum thrust of the engine. Now, just to define m bar over here is nothing but 1 plus f small f and small f is nothing but V e to a ratio. So, this gives you a slight correction that you need to do to the mass flow for the fuel addition into the combustion chamber. The areas are designated here a 1 is the entry area. So, that is the mass flow coming through the intake a e is the area of the exit at the exit phase of the nozzle and correspondingly P a and P e are the ambient and the exit pressures of the jet engine. So, that gives you the thrust that may be created by the jet engine and one can easily calculate if these parameters are made available for thrust estimation. The specific thrust which is normally a figure of merit for many of the jet engines is shown here in terms of C f which is nothing but f by m dot. m dot of course, is the mass flow that we have shown here and this is now designated in terms of V a into m dot into V e by V a that is the velocity ratio across the jet engine. So, V e by V a is nothing but the velocity ratio or the velocity enhancement through the jet engine minus 1 and this is the area ratio between the intake and the exhaust. This is P a by rho a V a entirely from the atmospheric conditions and the P e to P a the exit pressure ratio that may be available which in ideal case we know this could go to 1 and hence the second term could entirely go to 0. So, that is your specific thrust that you may like to calculate from the data that could be available for simple analysis of ramjet engine. What we see now from these equations which have been derived from fundamental principles that the specific thrust to be achieved a reasonable positive specific thrust to be achieved V e needs to be somewhat higher than V a. Now, this is what you know the operative velocity ratio is this can go to 1 and this could go to 0 and frankly we probably would not bother much about it, but this needs to be more than 1 and this needs to be as much more than 1 as possible. So, that you get a substantial specific thrust and as you can see if this is 1 the thrust generated will be 0 if this is less than 1 thrust generated will be negative. So, it is necessary that you have a substantial acceleration or velocity change through the jet engine to give you a reasonable amount of thrust. The other possibility of course, is if P a is more than P a, but the as we know if P is indeed more than P a your momentum thrust is going to come down. So, you have to keep an eye on both the values the best bet of course, is always that V e is substantially more than V a to give you more of momentum thrust. Now, we can look at the other normal figure of merit used for all jet engines and that is the specific fuel consumption. Typically, most of the engines you have already learned how to calculate thermal efficiency of an engine. However, most of the engines are designated or defined by their specific fuel consumption and the efficiencies often used as a figure of merit for the goodness or the badness of the particular engine. So, S F C is what we normally use as the engine efficiency figure of merit. Now, this is defined here as usual as before in terms of m dot f which is a fuel consumption divided by the thrust that is created and this comes out in terms of small f by C f which is the specific thrust and this is the fuel air ratio. So, if the fuel air ratio of a particular operating point is known and the specific thrust can be calculated we can get the value of S F C and that of course, stands for the as a figure of merit for the efficiency of the engine at that particular operating condition. The efficiency of the engine also can be of course, calculated as per basic definition of efficiency which is normally the thrust work that is created by the jet engine divided by the fuel energy that has been put inside the combustion chamber in terms of basic fuel energy or heat energy. So, Q F of course, is the heating value of the fuel in terms of kilo joules per kg and this is what gives you finally, the thermal efficiency of the ramjet engine. So, you can calculate thermal efficiency of a ramjet engine to designate thermodynamically what its efficiency value is. Now, we can look at having look at a basic ramjet engine we can take a look at some of the modern developments of ramjet engine. Many of these ramjet engines are now being developed in terms of very high supersonic flight applications and in those situations as you can see you are likely to have a very long intake. So, you have intake section which and then you have a long what is often known as an isolator that means, here you can see it goes through a huge number of shocks or what is often known as shock trains. So, these shocks obviously, diffuse the flow supersonicly hugely, but they are also loss making proposition. So, by the time the flow comes out through these shock train and gets delivered into the combustion chamber quite often and the combustion chamber as we see is indeed a subsonic combustor. The flow would have lost substantial amount of pressure having come through all these shocks and as a result of that the as we have just seen the definition of thrust and SFC and specific thrust the there will be some problem in terms of getting a good positive thrust out of this jet engine. So, some of the designs that people are now developing involve one for example, using some kind of a gas generated inside which could be a rocket or which could indeed be an embedded turbojet engine which operates only when it is required otherwise it can be switched off or it can be a rocket which is embedded inside which gives another jet out from here and that mixes with the combustor combustion chamber of the ram jet and two of them together create the high pressure high energy gas which then goes out through a nozzle. So, the combination can then go out through the nozzle to create a supersonic jet. The other option is to have a high pressure tank over here which has its own nozzle and from this tank you can eject high pressure gas and this high pressure gas coming out through this nozzle mixes with the combustor combustor gas of the ram jet and the combination then goes out through the ram jet nozzle again creating supersonic jet. So, many of these possibilities are now being developed and being are on the design board. One of the reasons is because we just discussed that coming through these various shocks the ram jet would be depleted of its energy and it may not be a very good jet engine device all on its own. Hence, a certain amount of help may be embedded within the jet engine configuration to provide additional energy which then can be harnessed to create more thrust during flying at very high supersonic speeds. At Mach 5 and above the normal ram jet cannot diffuse the flow any further to subsonic values for combustion purpose. As we were just discussing that if you have intake for high supersonic flights those intakes are full of shocks and as we have just seen they are full of shock trains. So, the flow is coming through a large number of shocks may be 8, 10, 15 shocks which are inside the intake system which includes an isolator. Now this isolator let us go back just for a minute this isolator actually is part of the ram jet and it is called isolator because it is a supersonic isolator which allows a long train of shocks before the flow is delivered into the combustion chamber and it also isolates the combustion chamber from the intake ambient pressure or temperature changes which happens with the change of altitude. So, this is often called an isolator because it is a long it houses a long train of shocks. So, when you have those train of shocks and if you keep on diffusing you keep on losing energy losing pressure. So, at above Mach 5 flight Mach number it is not very profitable to have that kind of shock train finally, delivering subsonic flow. So, what is quite often done now is the flow delivered is still supersonic. So, you do not make it subsonic you kill you keep it supersonic and deliver supersonic flow into the combustion chamber and hence the combustion designers have now developed a supersonic combustion phenomenon. So, this supersonic combustion is now embedded inside the ram jet engine and hence it is called a scram jet supersonic combustion ram jet. This now delivers the jet to the exhaust nozzle which then creates a supersonic flow. So, the combustion is now done in supersonic flow condition, but somewhat low supersonic flow. So, the flow is brought down from very high supersonic flow above Mach 5 to low supersonic flow near about Mach 1. And this isolator is needed to create the shock train. So, that a low supersonic flow can be delivered into the scram jet combustor. This is a physically rather long device a long duct through which the shock train is in which the shock train is housed. And the scram jet produces a useful thrust only after you have been able to do all that successfully to add very high flight Mach numbers above 5 and one is using scram jet these days for flights up to about Mach 8. We can look at a scram jet engine and indeed a scram jet powered vehicle over here. As you can see the flow is coming through the intake system and then you have let us say this part is a vehicle body and this is your jet engine. And outside the jet engine itself you have a vehicle body which is angled over here and it is often called the external ramp intake. Now, this intake system then has only one surface the other surface typically is not existing as a solid body before it enters the ram jet. Once it enters the ram jet you of course have the shocks immediately inside the ram jet vehicle ram jet engine itself. Now, this is normally integrated design of the vehicle and the ram jet. So, the vehicle body and the ram jet are almost designed in an integrated manner and they are housed in one single body typically under the belly of the flying vehicle. So, as the flow comes in it is isoprasonic is creating shocks over here and these shocks finally develop into the shock train and it goes through the isolator which is what we are talking about and this isolator through a large number of shocks diffuses the flow to low supersonic flow and then this low supersonic flow is delivered into the supersonic combustor. So, this is why it is called scram jet and then the combustion takes place and hot high pressure gas is then released through the nozzle which then creates the high velocity jet. So, this is coming out and again part of the nozzle has one single surface which is often called ramp nozzle because it is ramp is actually part of the vehicle body. So, the flow coming in through a ramp is part of the vehicle body, flow going out also is through the ramp which is part of the vehicle body and the other side of the surface is an open surface. However, we have a nozzle over here which is indeed again a convergent divergent nozzle and as a result of which you have a supersonic jet that comes out which is a hot jet and this jet has a velocity which is higher than the entry velocity. So, this is how a scram jet engine typically operates and gives thrust during high supersonic flights. Now, let us look at what is known as pulse jets. Pulse jets are very simple devices and they have been flown long back even during world war 2. Now, pulse jet actually operates under very simple principle that the flow which comes in comes in through valves. Now, inside the combustion chamber when the combustion is initiated the flow goes to high temperature and pressure and the flow is evacuated through a nozzle which could be a convergent or a convergent divergent nozzle and as it is evacuated these valves are forced open and the flow comes in. So, let us quickly understand how it operates. Initially a spark plug initiates the combustion process inside the combustion chamber and when the inlet valves are actually kept closed. So, the default valve position is closed and then the combustion takes place which raises the temperature and pressure to very high values because now the combustion is taking place in a enclosed volume and it is close to what can be called a constant volume combustion. So, you have very fast combustion very close to that of an explosion and very fast rise in temperature and pressure. So, it rises to very high pressure. So, this high pressure and temperature gas is forced through the nozzle and it creates a high velocity jet. Now, this creates the pressure drop inside the combustion chamber and as a result of this drop in pressure inside the combustion chamber the spring loaded valves inlet valves are open and then the air comes in through the intakes through these valves which are often the reed valves and the spring loaded valves are then closed again as soon as the combustion chamber is full and as I said the default position is closed and it can open only when a certain pressure differential actually exists across the valves. So, as soon as the combustion chamber is full the valves are closed and as a result of which you have operation let us go back quickly to the pulse state schematic. So, the flow comes in through the intake only when the valves are open otherwise they cannot come in and then the combustion is initiated and takes place in the combustion chamber and the flow is then forced out of the entire jet engine at high velocity through this jet pipe and as a result of which the thrust is created by Newton's principle or third law of reaction and when it is evacuated the flow comes in. Now, this thrust creates a motion for the jet engine and the jet engine attached to the flight vehicle and the vehicle moves and as the vehicle moves certain amount of air can attempt to come in it can come in only when the valve is open. So, this valve opening and closing is a crucial issue in the pulse jet operation and the typically operation of pulse jets operate at around 45 to 50 pulses per second. So, as you can see they are very fast pulses and as a result the thrust creation is indeed quite fast. So, you can create a very fast pulses and the jet engine can operate in a pulsating manner to create almost continuous thrust generation. Now, since now the combustion is not dependent on the intake ram compression pulse jet can be used for take off and landing. So, this is a big advantage over ram jet you can use a pulse jet engine for actually taking off and landing of an aircraft it has been used in the world war 2 during by the Germans for flying their vehicles powered by pulse jet because it does not need ram compression for its combustion and nozzle operation. Let us look at the fundamental thermodynamics that you have done very quickly to the ram jet operation. You can I have quickly written down here all the steps that goes through this is of course, your compression that it takes place and then you have constant volume combustion and then it takes it to very high temperature and from where it is released through the nozzle to create high velocity jet and then this is of course, your constant pressure return path which is through the atmosphere. So, you have a constant volume combustion and a constant pressure return path. So, this is one of the heat engines where you have a dual process of constant volume combustion and constant pressure return path. So, the pressure is operational and you can find out from the isentropic laws the value of the pressure this is the ideal pressure generation the real pressure actually uses. So, p 0 2 actually would have a efficiency of the intake process through the valves embedded into its equation. So, this is the efficiency with which the valve is allowing the flow to come in and then you have the pressure generation through the combustion process because of the rising temperature and as a result of which you get very high pressure and temperature. So, this is not a constant pressure this is a constant volume combustion and this is from your equation of state and now you can write down the work balance or the energy balance this is the energy with which the air came in and this is the fuel energy of the burning of the fuel multiplied by the combustion chamber efficiency and this is the energy of the gas with which the gas is now going out. So, from this energy balance you can write down the fuel air ratio with the help of the various values of C p of gas the temperature of the gas the C p of air with which it came in and the temperature of the air with which it came in the heating value of the fuel the combustion chamber efficiency other C p of the gas and the temperature of the gas. So, all that would give you the fuel air ratio and from which you can write down the total temperature ratio the total static temperature ratio which would be equated to the total total to static pressure ratio from which you can now get the velocity of the exhaust jet and that from your isentropic relations you can write down the velocity of the exhaust jet in real cycle P is not equal to P a in ideal cycle they would be equal to each other and now again you can write down the thrust equation more or less the same way that we have written in other jet engines including the ramjet engine which we have done just a few minutes back and the specific thrust exactly the same way you can write down the specific thrust equation and you can write down the thrust specific fuel consumption which is as I mentioned the figure of merit for all jet engines. So, you can write down all those parameters the performance parameters thrust specific fuel consumption specific thrust all those things with the help of simple cycle analysis that you have done in your earlier lectures. So, this is a very simple device the ramjets and the pulse jets with the help of which you can create a jet engine you can create thrust and you can create a vehicle powered by ramjets and cramjets and pulse jets can actually fly. Now, this is obviously a very simple option that we have ramjets and scramjets as we have seen cannot take off and land but pulse jets can they are not dependent on ram compression. So, we have very simple versions of jet engines without compressors without turbines one of them the pulse jets can take off and land but obviously, they cannot operate at very high supersonic Mach numbers the ramjets can operate at high supersonic Mach numbers and the scramjets can go to even higher supersonic Mach numbers. So, we have just dealt with certain simple devices simple jet engines which can operate under various operating conditions creating jet thrust using the jet principle of creation of thrust without the aid of compressors and turbines and these jet engines all of them actually have been made and flown and they have actually flown the various kinds of aircraft and scramjets are still being developed to fly very high supersonic vehicles in the air in the atmosphere. So, we have just gone through a large number of jet engines which give you thrust for flying craft main aircraft or missiles or other kinds of crafts through the atmosphere because they use air as they are all air breathing engines and they are all jet engines. Next we shall be considering a jet engine which is not an air breathing engines we shall be talking about rockets and we shall be talking about rocket propulsion and rocket engines and this is what we will be doing in the next class where we shall open up a chapter on rockets.