 Now, you may recall from our earlier discussion of mixing chamber and the open feed water heater that the mixing chamber is a strategy for increasing the temperature of stream without directly heating it. So, basically there we had steam and then the liquid which we wanted to heat the two are mixed together and the exiting stream was still compressed, still liquid but at a higher temperature. So, that is a strategy. Now, mixing certainly is irreversible. So, there will be exergy destruction as a result of mixing, but the hope here is that heating the stream by mixing it with the high temperature steam would be much more efficient or would cause lesser exergy destruction than heating it in a high temperature reservoir that is the hope and that is what we will try next. This strategy is called regenerative feed water heating. It is called regenerative feed water heating. The basic idea here is to accomplish an increase in the enthalpy of the feed water using steam that has been extracted from the turbine after undergoing partial expansion. So, we extract some of the steam from the turbine after it undergoes partial expansion and then mix the feed water before going into the boiler with the steam so that the temperature of the feed water is increased and the amount of heat that we have to add in the boiler will be reduced as a result of the strategy and the external irreversibility due to temperature difference will also go down because the feed water will now enter the boiler at a higher temperature than before. Earlier it was entering at almost condenser temperature maybe just slightly above condenser temperature now it will be at a much higher temperature compared to the condenser temperature. So, hopefully this will reduce the rate of exergy, this will definitely reduce the rate of exergy destruction in the boiler. So, this reduces the heat to be added in the boiler but the downside of this strategy is that since you are extracting part of the steam from the turbine before it undergoes full expansion the amount of work that is developed in the amount of power that is developed in the turbine also decreases. Now, the enthalpy transfer or the heating of the feed water can be accomplished in two different ways. One is of course mixing. So, we take the steam that is extracted from the turbine, take the feed water that is coming from the pump, mix them together and then the stream leaves at the extraction pressure. So, everything is at constant pressure and we will see that now. The other strategy is to use the so-called closed feed water heating. We will see this also. Let us start with open feed water heating. So, here as this block diagram shows the the steam enters the turbine with a considerable amount of super heat it then undergoes expansion. Now, part of the steam is extracted here. So, this is at the extraction pressure and sent to the feed water heater. Now, the feed water which has been pumped from the condenser pressure to the extraction pressure enters the feed water heater where these two streams are mixed together and then saturated liquid at the extraction pressure leaves the feed water heater. It is then pumped to the boiler pressure and the cycle is repeated. Notice that the feed water heater because it is an open feed water heater where streams are mixed all the streams have to be at the same pressure. So, this is at extraction pressure and this is also at the extraction pressure. It is not pumped to the boiler pressure, but it is pumped to the extraction pressure and the leaving and the stream that leaves the feed water heater is also at the extraction pressure. So, the feed water heater operates at constant pressure which is equal to the extraction pressure. Let us take a look at this on a TS diagram. So, the expansion in the turbine is from 1 to 2 hours for part of the steam. So, let us say X kg per second of steam is extracted from the turbine. So, that undergoes expansion from the boiler pressure to the extraction pressure. So, notice that this is the extraction pressure. This is the boiler pressure and this is the condenser pressure. So, part of the steam that is X kg per second is extracted from the turbine. The rest of the steam 1 minus X kg per second undergoes expansion up to the condenser pressure. Now, this is then taken to the condenser where it exchanges heat with the ambient, loses heat and then it leaves the condenser as saturated liquid at condenser pressure. It is now pumped to the extraction pressure, not the boiler pressure. It is now pumped to the extraction pressure and taken to the feed water heater where it is mixed with the steam which is coming from here. So, the steam which was at state 2 S which was slightly super heated as it loses heat it condenses at constant pressure and this liquid water which is a compressed liquid is now heated from state 5 S to 6. So, at the exit we have saturated liquid at the extraction pressure. So, the mass flow rates of the extraction and the liquid water are adjusted. In other words, the extraction mass flow rate is adjusted so that at the exit to the feed water we get saturated liquid at the extraction pressure which is then pumped to the boiler pressure and then again it goes back to the boiler pressure. Notice that the water when it enters the boiler now is at a much higher temperature than it was before. So, this should definitely reduce the exergy destruction in the boiler and hopefully the second law efficiency of the cycle will go up. First law efficiency may go down it is possible because we are now losing some of the work that we could have produced in the turbine. So, let us work with some real numbers and then see what happens. So, we will take the same cycle that we had before keeping the boiler pressure and condenser pressure the same and other things the same and then see the effect of open feed water heating. So, state 1 is the same as before state 2 S again is now at the extraction pressure 3 S is the same as before that is at the condenser pressure same specific entropy as S 1. So, that is the same as before state 4 is the same as before. So, let me just maybe show this with a slightly different color. So, this is different from before. So, state 2 S is different from before other states are same as same as before. Now 5 S is different from before because 5 S is at the extraction pressure and not the extraction pressure and not the boiler pressure earlier it would have been at the boiler pressure. So, this is different state 6 and 7 S of course, were not present in the previous cycle at all, but this is saturated liquid this is compressed liquid at entry to the boiler. So, the extraction amount of steam to be extracted from the turbine may be obtained by applying SFE to the feed water to the feed water heater and we get and this gives us X to be equal to 0.313. So, for every kilogram per second that enters the turbine we extract 0.313 kilogram per second after partial expansion to a pressure of 40 bar. So, heat supplied in the boiler or rate of heat addition in the boiler may be evaluated like this H 1 minus H 7 S, which is 2363.17. Let us see 2363 compared to 3260. So, you can see that there is a considerable reduction in the amount of heat that is being added in the boiler. Heat rejected 1284.1 notice that heat rejected appears to be less only because of the reduced mass flow rate through the condenser. The state points remain the same. So, if you look at the regenerative cycle state point 3 S and 4 are the same as before as we have mentioned, but because the mass flow rate is reduced the rate of heat rejection heat rejection in the condenser is less. Now, what produced by the turbine comes out to be 1096 what is that the extracted steam undergoes expansion only up to the extraction pressure and 1 minus x undergoes expansion from state 1 all the way to the condenser pressure. And the turbine work decreases. So, this is 1096 compared to 1407. So, 1096 compared to 1407. Now, we have two pumps, one which is pumping from the feed water heater to the boiler, another one which is pumping from the condenser to the feed water heater. So, the total work supplied to the pump is power supplied is 17.8 kilo joule per kilogram. Net power is 1079 and the thermal efficiency of the cycle comes out to be 45.66. So, you can see that the efficiency of the cycle has actually increased. Although the work output from the turbine has decreased, the reduction in the heat added in the boiler is more than that so that the overall efficiency of the cycle has actually increased. So, regenerative heat feed water heating improves the efficiency of the cycle. Although the specific power output decreases. Remember we said three matrix, specific power output efficiency of the cycle, second law efficiency. Now, efficiency of the cycle has improved. Let us look at second law efficiency. So, rate at which exergy is supplied may be calculated in the same manner as before. So, we get this to be 1535. TH remains the same because we have not changed the boiler pressure or increased the degree of superheat. We have maintained it the same to enable a fair comparison. So, rate at which exergy is recovered comes out to be this. So, the second law efficiency is now 76.69. So, it has almost come back to the same value as what we saw for the basic cycle. And so, this suggests that the rate of exergy destruction in the boiler is less. And that turns out to be the case. It is 262.32 compared to 584.15. So, it has almost half of what it was before. But there is additional exergy destruction now in the feed water heater because we are using a mixing process. So, it is that comes out to be 95. So, 262 plus 95 comes out to about 357. So, 357 kilo joule per kg is the total exergy destruction, additional exergy or total exergy destruction. Now, we have to compare that with, I am sorry, we have to compare that with 584. It is still considerably less than the 584 that we saw without regenerative feed water heating. So, as we said before feed water, the improvement in efficiency and the reduction in the exergy destruction in the boiler is because the feed water enters the boiler at a much higher temperature than before. So, what we will do next is to discuss closed feed water heater. So, open feed water heater as we already said operates at the same pressure. So, the entering steam is at the extraction pressure, the entering liquid feed water is also at the extraction pressure and the heated feed water leaves at the extraction pressure. Now, closed feed water heater is more like a heat exchanger and that can operate with different pressures for the extracted steam and the feed water. So, we will take a look at that strategy also. Next, before we move on to address the shortcoming with the regenerative feed water heating. The shortcoming of the regenerative feed water heating is that the specific work has decreased. So, the specific work has decreased. So, we need to address that. The first law efficiency has improved, second law efficiency has also improved. So, what we need to look at now are strategies for improving the specific power when we add regenerative feed water heater.