 two topics and those are modification of cycles and seven combination of cycles. It all depends on the time we have in the course on thermodynamics to do these type of things. Quite often modification to cycles and combination of cycles is left appropriately to a course in applied thermodynamics or to a course in energy conversion. However, when it comes to the modifications of cycles you tell them that each modification must be looked at depending on what does it do to the efficiency or the coefficient of performance. So, there are some modifications which will try to improve the efficiency and the coefficient of performance. Some modification will try to improve the specific power output whereas some modification would essentially be technical modifications to improve the life of the components. And it turns out that the modifications are always good for some aspect, bad for some aspect. There are some modifications which will improve the efficiency but they will decrease the specific output. Some modifications would improve the efficiency as well as the specific output but will not be so good from the technical point of view. When it comes to power plants modifications are found typically in the Brayton cycle and the Rankine cycle whereas in the Otto and Diesel cycles there are hardly any modifications perhaps may be because we are constrained by the mechanical complexity of the device. Remember that Brayton Rankine cycles or their corresponding refrigeration cycles are multi-equipment cycles. They are various pieces of equipment connected together, linked up together through pipelines and ducts. And when you have such a duct work something like a fluid thermal fluid circuit it is easy to put a component in between or modify the connection and add a few components somewhere whereas in a single equipment cycle like our internal combustion engines it is difficult to modify anything because rather than just the thermal and fluid modifications a lot of mechanical modifications will also have to be done. In the Brayton cycle the common modifications are reheat, intercooling which is not really so common and regeneration. In Rankine cycle I have shown so far Rankine cycles working on superheated steam. Some people say that is the basic Rankine cycle and the first modification they talk about Rankine cycle with superheating but then you have reheating. You do not have anything like intercooling in a Rankine cycle because the job of intercooling is to reduce the power absorbed by the compressor and since the power absorbed by the pump in a Rankine cycle is very small compared to the power output of the turbine it does not make economic sense to try to reduce that to any extent and of course regeneration. And what the good idea to do is to start with the Rankine superheating then go to Brayton and Rankine reheating you can do it almost together because they are very similar in characteristic. Then go to Brayton intercooling there is no Rankine intercooling and then you do Brayton regeneration and Rankine regeneration in order because the scheme for the Brayton regeneration which uses a heat exchanger and the Rankine regeneration which uses extraction from the turbine and feed water heating are at least on the face of it and in implementation rather different. And then you go to corresponding modifications in joule cycle and vapor compression cycle. For Rankine superheat all that you do is when you actually tell these two students it is always a good idea to solve an illustrative problem along with this. Let us say this is the high pressure line this is the low pressure isobar and our normal Rankine cycle is like this. In superheating what we do is we do not stop with saturated steam we go to a certain temperature in the superheat zone and then expand it in the turbine. So, this turbine state line get shifted to a slightly higher entropy. The reason for doing this is as follows we know that the Rankine cycle is similar to the Carnot cycle except for a modification here. But remember that as you go to higher and higher temperatures expecting higher and higher efficiency the cycle becomes narrower because the latent heat which is represented by this distance is actually this is data this is SFG we will have to multiply it by T. But notice that as you approach the critical point the latent heat goes on reducing and then the cycle will become narrow and we will not get any advantage. So, what we do is typically this is restricted to approximately 130 bar 132 150 bar. So, this will be the saturation temperature at about 130 bar but that temperature is a bit too low when we burn fuel say for example coal we can easily achieve temperatures at this state 3 of 700 800 degrees C and the saturation temperature at 130 bar which will be of the order of 300 degrees C let me see what it is 130 bar is 330 degrees 330.9 degrees C at 150 bar is 342.2 degrees C remember that the critical temperature is 374 degrees C. So, we are below the critical temperature and significantly below the critical pressure of 221 bar. So, we allow in the boiler that the steam be superheated and although I said that we can reach 700 800 degrees C today we do not have materials which continuously will withstand that temperature in the superheater of a steam power plant. Consequently the temperature at 3 today is restricted to less than 600 degrees C to typically be 570 580 560 degrees C of that order but anyway when we go from a temperature of 330 to a temperature of say 580 we are increasing the entropy we are increasing the temperature we are increasing the heat absorbed in the boiler but we are increasing also the enthalpy drop in the turbine. Consequently superheating usually does the following things for us T3 increases but it is restricted to less than 300 600 degrees C today just from materials consideration no thermodynamic consideration is involved the cycle efficiency improves specific power improves and another improvement is the dryness fraction at the exit of the turbine that also improves and that is good from the life of the turbine because although turbines can handle wet vapour the wet vapour which actually flows like droplets of liquid water in a moving stream of dry saturated stream those droplets have an eroding effect on the last stages of the turbine and hence all these things are good for the plant and hence superheating is a very very common thing to do in Rankine cycle plants in fact major power plants you will never see now saturated steam except one exception and that is nuclear power plants because the nuclear reactors do not create heat at very high temperature and that is why there we use comparatively low pressure low temperature saturated steam Rankine cycles or the bad thing here is the near the state 3 the super heater tubes are at such a high temperature and also remember this is a point of high pressure high temperature so super heater tubes are under a tremendous stress and because of that their failure rate is high and if you see the cause of failure or taking power plants offline for maintenance vast majority of the incidents are caused because of super heater tube failure we are thermal engineers but we are all mechanical engineers recommended reading for all of us are two novels by Arthur Hilly one novel is known as overload and you will get enough information about power plant super heater tube failures and so on and the other knowledge other novel is wheels which is about design and development of cars as thermal engineers we should definitely read overload as mechanical engineers we should definitely read overload as well as wheels so that is about the super heating modification of Rankine cycle then we come to the next modification which is reheating can be implemented in the open cycle the Brayton cycle type can be implemented for vapor clothes cycles if you look at super heating super heating does not have a corresponding thing in Brayton cycle because there is no evaporation there everything you are already in the super heated zone but when it comes to reheating the Brayton cycle and Rankine cycle are modified in a similar way you have to add some equipment and usually efficiency improves usually specific output improves and hence wherever possible super heat is also employed if you look up the Brayton cycle on the TS diagram so this is the TS diagram and let us say this is the high pressure line the low pressure line for the Brayton cycle the original Brayton cycle would be something like this 1 2 3 4 should really show 4 to 1 it is considered to be an open cycle now notice that the maximum temperature is at 3 but why is it restricted it is restricted again from material consideration but if you look at the possibility of raising the temperature you can take the temperature much beyond 3 because if you take the stoichiometric fuel air fuel ratio for typical gas turbine fuels it will be of the order of 13 or 14 however if you burn that much fuel the temperature which you will reach is almost the stoichiometric flame temperature and parts of the gas turbine will simply melt so we burn lesser fuel typically half of this or even less than that in a gas turbine plant just to restrict the temperature at T3 that means the oxygen in the air is not completely used up when the gas enters the first stage of the turbine and since the oxygen is still there you can burn more fuel and we do that not immediately but what we do is between say pH and PL we select an intermediate pressure say PI and in the first turbine say the high pressure turbine we expand the fluid only up to PI call this as the new 4 remove this part and then we heat it up to 5 there is no reason why 5 cannot be as high as 3 if the presence of air permits it and it usually permits it so you add Q1 here in the main heater so Q1A and then in the reheater you add Q1B Q.1B so the heat supply is now in two parts one in the main combustion chamber from 2 to 3 and then in the reheating combustion chamber from 4 to 5 then you pass it through another turbine 5 to 6 and then either you exhaust it to air or if it is a closed cycle put it through the cooler. Now the turbine output also is in two parts HPT and LPT compressor remains unchanged this is the reheating modification of the Brayton cycle in case of Rankine cycle it is slightly different let me say that this is the vapor form again I am showing it T as diagram. Let us say this is the lower pressure line this is our boiler line and we go up to this temperature for super heating say 1, 2 and 3 instead of expanding straight up to the condenser pressure what we do is we select an intermediate pressure pH PL PI we select an intermediate pressure expand the steam first in the high pressure turbine then take it back to the boiler in a component of the boiler called the reheater and again heat it up to say first turbine high pressure turbine exhaust it at 4, 4 to 5 reheating and 5 to 6 expansion in the second turbine one should be able to sketch I am not doing it I leave it to you as an exercise to sketch the appropriate block diagrams for the reheating modification for the Brayton cycle and the Rankine cycle for the Rankine cycle if reheating is done you will have to add first split the turbine into two parts and HPT turbine and then LPT turbine and then duct the steam back to the boiler for reheating and duct it back to the turbine so additional equipment and additional connections are needed. But efficiency will improve specific output will improve the dryness fraction at the exit of the turbine will improve x4 and x6 it will always be higher than the earlier x4 then comes the intercooling this is done only in the Brayton cycle and this reduces W dot C I draw only this part 1 to 2 is the compressor straight line other part remains the same whatever modifications you have it is an unmodified Brayton cycle so instead of compressing in one shot from PL to PH what you do is select an intermediate pressure PI compress it only up to that point so second part of the compressor is removed from 1 to 2 but 2 is now at PI now you put it through a heat exchanger where the temperature is now again reduced back to near ambient calling 3 and then you have the high pressure compressor where it is again increase to 4 so you will notice that the temperature at 4 now is much lower than the temperature at 2 which was the earlier 2 here at this point now from 4 it enters the combustion chamber the remaining part remains the same except that because I have changed the nomenclature the intercooling reduces the work done by the compressor but in intercooling increases Q dot 1 and hence intercooling does not always improve the efficiency it depends on the relative ratio of reduction in compressor work 0.4 no 0.4 need not be the question is whether 0.4 and 6 are dry saturated vapor is no need it may look like that but usually 0.4 is just in the vapor zone but need not be it could be slightly superheated but most often it is at a dryness fraction of around 0.95 the issue is not the issue is from the turbine design point of view where the intermediate pressure lies that is a design parameter for the turbine designers otherwise there is nothing special about 0.4 and 0.6 do not be under the impression that they have to be dry saturated steam so here W dot C reduces but your Q dot and this means that W dot net will improve because W dot turbine is not changing Q dot 1 increases so since both are increasing we are not sure whether the efficiency improves or decreases depending on the way it is implemented and other parameters efficiency may go up efficiency may also go down and since this is a heat exchanger in which the temperature difference the intercooler from 2 to 3 is a heat exchanger with a rather small temperature difference temperature at 2 it may be you know even less than 200 degrees C so we do not have much of a temperature difference air is flowing on one side so the intercooler turns out to be a rather bulky heat exchanger and hence intercooling is not as common as is reheating or regeneration there is no intercooling in the Rankine cycle so now we come to the idea of regeneration we have already come across the idea of regeneration in Ericsson cycle and Sterling cycle where during say in Sterling cycle during a constant volume cooling process since it is a reversible process heat needs to be rejected but you cannot have the heat transfer there with the environment so what you do is you store the heat in a heat exchanger matrix and make it available at the corresponding temperature as the working fluid gets heated as in the other process in the heating process which is also constant volume so regenerator can use heat exchangers and the regenerator is employed both in Brayton cycle and in Rankine cycle it is more common in Rankine cycle than in Brayton cycle and there is a simple reason why is it so the idea of regeneration in the Brayton cycle it is something like this let us say that we have a Brayton cycle with not a very high pressure ratio let us say that our Brayton cycle otherwise unmodified like this now what we notice is heat is being supplied from T2 to T3 whereas heat is being rejected or hot gases are being exhausted at T4 it is rejected from T4 to T1 and the question that is asked is if T4 is higher than T2 then why not use the exhaust heat at 4 for increasing the temperature of 2 to some extent why use your fuel to start heating it from 2 itself and that is the idea which leads to regeneration and what we do is we set up a heat exchanger between this stream and this stream so that in ideal case we can raise this temperature to 4 prime and hence our Q dot 1 now is required only for heating it up from state 4.23 if our regenerator is a good heat exchanger temperature at 4 prime will be almost equal to temperature at 4 otherwise it will be slightly less similarly the gases will now be cooled to 5 and from there it can be exhausted or you can use a cooler to cool it from 5 to 1 so this requires use of a use a heat exchanger which is known as a regenerator and because of this Q dot 1 reduces reasonably significantly there is no change in W dot because we are not modifying the turbine and the condenser at all and hence your efficiency improves the specific output does not change because W dot net does not change the disadvantage of this is that the regenerator or this heat exchanger is a gas to gas heat exchanger now when students do a course in thermodynamics they have not done a course in heat transfer so they do not have any idea of the sizing of a heat exchanger but we know because we have studied heat transfer also is that the heat transfer coefficients pertaining to gases are low hence a gas to gas heat exchanger will be a very bulky affair and that is the reason why people are reluctant to implement regeneration in a Brayton cycle and particularly those Brayton cycle which are used in aircraft as the jet engine cycle or its modification will never use a regenerator only stationary cycles ground based which are used in gas turbine power plants may use a regenerator the regeneration in Rankine cycle is done in an entirely different way this is known as heating of feed water or simply feed heating regenerative feed heating I will leave it again as an exercise to you to draw the block diagrams for Brayton cycle with reheat Brayton cycle with intercooling and Brayton cycle with regeneration you can have more than one modifications together so in principle you can have a Brayton cycle will reheat Brayton cycle with regeneration and Brayton cycle with intercooling all together it will be a very complicated cycle but in principle that is possible so in Rankine cycle feed heating what is done is the following here the idea is extraction of steam from the turbine and this extracted steam is either mixed or is otherwise used increase the temperature of feed water that is the water which is entering the boiler hence you reduce the load on the boiler and hence you improve the efficiency let us see how it is done let us first show a block diagram let me show first that the block diagram of an unmodified Brayton cycle will be like this boiler may be superheated steam we have a turbine we have a condenser we have a pump and we complete the circuit this is unmodified Rankine cycle the aim of regenerative feed heating is to raise this temperature in an unmodified Rankine cycle the temperature at this stage one state one is the saturation temperature at condenser pressure which is very near ambient temperature and the pump does not raise it much may be by a few degrees so the temperature at this point two is not very high and boiler receives water at that temperature and has to do the job of raising the temperature of water from two to the saturation and then beyond that to superheat so what we do is we modify this the simplest modification is as follows we take an extraction from the turbine that means if m dot not is the steam going into the turbine after a few stages we extract steam equal to m dot e a small fraction a few percent may be 10 12 percent the rest of the thing goes through the remaining part of the turbine because of that you will notice that w dot t for a given m dot will now reduce a bit then the pump one to two pumps it into an intermediate pressure in which in a mixing chamber called a contact heater this feed water is mixed with this steam and because we have to finally go to the boiler pressure we have another pump so you have a pump one which pumps it from condenser outlet to the intermediate pressure then you have what is known as a contact heater in which this feed water is mixed with the extraction and where you have a pump two which pumps it to after contact heater the mixed state is three after the pump it is four say turbine inlet is five extraction is six turbine exit is seven on the next page I will show you the T s diagram of this now the question is how much extraction shall we manage for shall we have remember that these pumps we have to see to it that they pump only liquid those of you who are conversant with fluid dynamics and fluid machinery would realize that for a liquid pump what we say NPSH has to be maintained that means a net positive suction head has to be maintained otherwise pumps will cavitate they are and because of that they will either not work properly or apart from improper working they may damage themselves so because of that the condenser exit at one is saturated liquid and the inlet to this this is inlet to the first pump the inlet to the second pump is also maintained at saturated liquid and hence the extraction here is adjusted by means of a control valve to see to it that temperature at three it saturated liquid at that pressure with this understanding we will now sketch the T s diagram of a regenerative PDT Brayton cycle let us say this is the condenser pressure let us say this is the intermediate pressure and let us say this is the boiler pressure so this is P boiler this is P condenser and this is P extraction and let us say that we start our turbine expansion from this point what was that point here 5 6 7 is turbine so let us say that the turbine state line is state 5 to state 6 to state 7 and we condense whatever comes out at 7 and bring it to 1 but from 5 to 6 to 7 to 7 to 7 to 7 to 6 the mass flow rate is m dot we extract the mass flow rate equal to m dot e here what goes to the remaining part of the turbine is m dot not minus m dot e and that is what condenses what condenses is also m dot not minus m dot e now at this stage we pump it pump it to 2 and then in the mixer this point 3 is a mixed state of 2 and 3 2 and 6 giving you 3 notice here 2 and 6 2 here 6 here giving you 3 and you will notice that the mass flow rate is if I have a stream at 2 and a stream at 6 if I hardly have any extraction then the resulting point will be very near 2 if I have a lot of extraction then the resulting point will be nearer 6 so I adjust the extraction in such a way that 3 it saturated liquid at the extraction pressure P and then you have the second pump 1 2 2 is the first pump 3 2 4 is the second pump and at 4 the stream enters the boiler and notice that if I was not to have an extraction the boiler entry would have been here now instead of that we have it at 4 so now the amount of heating done in the boiler is reduced and you can say that the low temperature part of heating in the boiler has been deleted so the mean temperature of heat input into the boiler has also gone up and because of this the efficiency improves but because we are extracting something the specific power output goes down however the efficiency improvement is significant and hence in a reasonable size plant feed heating is invariably employed the calculation would proceed as follows you will have to determine after having determined all state you will have to determine m dot 3 as follows you apply first law to the mixer so called contact heater there is one stream going in at state 2 extraction coming in at state 6 m dot e what comes here is m dot naught minus m dot e what goes out is the sum of this m dot naught it goes out at state 3 so if you apply first law assume that this is working in a steady state and that potential energy changes and kinetic energy differences are negligible then you will get h 6 m dot e plus h 2 m dot naught minus m dot e is h 3 m dot naught we solve this equation for m dot e when we know m dot naught and now remember the power output will be w dot t plus w dot t minus w dot t w dot t needs to be now written in terms of two components m dot 0 going from 5 to 6 m dot 0 minus m dot e going from 6 to 7 so we have m dot naught going from 5 to 6 plus m dot naught minus m dot e going from 6 to 7 similarly w dot p is in two parts first you will have m dot naught minus m dot e h 2 minus h 1 plus that means again with a negative sign minus m dot naught going from h 4 minus notice that in the previous figure m dot naught minus m dot e being pumped from 1 to 2 and m dot naught being pumped from 3 to 4 and this q dot supply q dot 1 will now be m dot 0 h 5 minus h 4 the ratio of these two will give you the efficiency of the plant and w dot net divided by m dot 0 divide this equation throughout that will give you specific output what I have indicated here is only the contact heater in my exercise sheet I think there are exercises on perhaps there are exercises on other heaters there are only two contact heaters there are other types of heaters but I think in a thermodynamic course you may just talk of contact heater there are other heaters flash heaters for the more common drain cooled heaters but we usually leave those things to the course on applied thermodynamics or power plant engineering energy conversion whatever you call it I think in a thermodynamic course this is perhaps all one should do in the cycles part of course you can do modifications in the exercise sheet you will find modifications for refrigeration plant also and you will have one thing I did not try tell is that in the exercises you can ask them to do calculations with isentropic efficiency of various components particularly turbine and compressors and hence the effect of those component efficiencies on the power plant performance can also be studied but remember if you are teaching cycles in a thermodynamic course then there is no need to go deeper into component characteristics and much more deeper into the cycle parts you lay out the cycle you tell what the component characteristic is student conversion with thermodynamics should be able to find this way that is about it let me see 0.4 should be dry vapor line that is not true then why CC and 22 says will the efficiency in reheating increase or decrease in Brayton or Rankine cycle with reheat the efficiency usually increases but of course you can always create a situation where it may decrease but reheating is common and it almost always increases the efficiency and improves the specific output.