 So, we saw the open feed water heater and we mentioned the fact that the streams that come into the feed water open feed water heater and the stream that exists are all at the same pressure. In fact, the feed water heater operates at the extraction pressure of the from the turbine. So, the fluid that enters the feed water here the feed water that enters the heater and the extracted stream are at the same pressure and the feed water that leaves the heater afterwards is also at the same pressure. So, this is a requirement because all these are being I mean the streams are being mixed physically in the feed water heater. Now, in contrast in the closed feed water heater the pressure of the different streams can be different from each other. So, here we are showing a closed feed water heater. So, as before the part of the steam is extracted from the turbine at extraction pressure. So, this would be at the extraction pressure. Now, you may notice that the feed water that enters the feed water heater is at the same pressure as the boiler pressure, not the extraction pressure, but the boiler pressure. So, it actually goes through in a separate path and never mixes with the steam from the turbine that has been extracted from the turbine. So, it can be at a different pressure. So, it is usually at the boiler pressure, whereas the steam that enters the feed water heater is at the extraction pressure. So, the feed water as it moves through the heater is heated by the steam that enters here. And as the steam transfers its enthalpy to the feed water condensers and there is a condensate or saturated liquid at the bottom of the feed water heater. Now, there are two strategies that are available for handling the saturated liquid condensate at the bottom of the feed water heater. One is to throttle it to the condenser pressure and send it to the condenser itself or pump this condensate using a pump to the boiler pressure and then send it to the boiler along with the feed water heat along with the feed water that exists from the feed water heater. So, one strategy is to throttle it send it to the condenser where it is again pumped to the boiler pressure, but sent to send through the feed water heater. The other strategy is to pump it separately using another pump and then send it to the boiler directly. So, as you can see, since the streams are never mixed, the streams can be at different pressures and they are usually at different pressures. So, the tears diagram of Rankine cycle with close feed water heater looks like this. So, we extract part of the steam from the turbine and this is sent to the feed water heater. So, depending upon whether the condensate is throttled and sent back to the condenser or whether it is pumped directly to the boiler, we have either 1 minus x kg per second or 1 kg per second in this part of the cycle. So, the pump then pumps this to the boiler pressure and it then traverses through the close feed water heater when it is heated to higher temperature corresponding to state 6 and then it is sent to the boiler. So, further heat addition takes place from state 6 to state 1 in the boiler. Now, in case the condensate is pumped separately to the boiler pressure, there is additional heat that is going to be transferred to take the feed water from state 8 to state 1. So, depending upon how this is handled, the amount of feed water that is pumped in this pump is can be 1 kg per second or 1 minus x kg per second. So, we can either have two pumps or one pump and different designs utilize, I mean different plans utilize different designs but both are equally effective and basically the close feed water heater has almost a same sort of performance as the open feed water heater when it comes to overall performance parameters of the cycle. Now, I have not really worked out an example involving the close feed water heater here primarily for sake of brevity but the textbook has worked example with the close feed water heater and those who are interested or urged to consult the textbook and work out the example that is given there. Whether it is a closed feed water or open feed water heater regenerative feed water heating definitely results in an improvement of the thermal efficiency. However, this comes with the price and that is a reduction in the specific work output or net work output whichever one you want to look at. If it is net work output that you are thinking of then we can simply address this issue by increasing the mass flow rate. So, if the net work goes down by a certain amount we adjust the mass flow rate, we increase the mass flow rate so that the net work is whatever we want it to be. The downside of this strategy is that the equipment size will have to increase now to accommodate the increased mass flow rate and that is generally not desirable. So, what we would like to do is retain the advantages of regenerative feed water heating namely increase in thermal efficiency of the cycle, increase in second law efficiency of the cycle but address the shortcoming which is reduction in the power output. This can be addressed or this is usually addressed in practical applications by resorting to reheating of the steam. So, this addresses the shortcoming that we have with regenerative feed water heating and we will take a look at this next. So, what is done here is the following. So, in regenerative feed water heating whether closed or open we had the same setup basically we had a single turbine and steam was extracted partially from the turbine. So, you can see that steam was extracted from the turbine before some of the steam is extracted from the turbine before it undergoes full expansion. So, the same is done in closed feed water heating also as you can see here. But when reheat is incorporated what is generally done is that rather than extracting part of the steam from the turbine the turbine itself is split into two parts. So, we have one turbine that is like this and the stream that comes out of this is partly sent to the feed water heater. The rest of the steam is taken to the boiler where it is reheated and then sent to another turbine which would look something like this. So, the first turbine is usually called a high pressure turbine and the second turbine is usually called a low pressure turbine for obvious reasons because the pressure at entry to this turbine is the boiler pressure which is quite high whereas, the pressure at entry to the low pressure turbine is less than the boiler pressure because the steam has already undergone expansion in the high pressure turbine. So, that is the major difference that you see in the expansion site in the cycle when reheat is incorporated. So, you can see that the steam expands entirely from the boiler pressure to an intermediate pressure. So, this is the boiler pressure and this is the condenser pressure. So, what we use to call extraction pressure is now called an intermediate pressure. So, the steam is expanded in the high pressure turbine up to the intermediate pressure then part of the steam is extracted and sent to the feed water heater. The rest of the steam is then sent to the boiler where we have a heat addition process from 2 S to 3. So, heat is added and the temperature of the steam then increases. Usually, the temperature is increased up to the same temperature as state bond. Typically, although we have not shown it that way in this illustration, typically that is what is done. And then the steam is sent to a low pressure turbine where it undergoes further expansion up to the condenser pressure. And the cycle is then the same as open. So, what we have shown here is reheat with open feed water heater. So, this additional heat supply in the boiler should increase the work output when the steam undergoes further expansion in the low pressure turbine. So, the idea is we keep all the beneficial aspects of regenerative feed water heating while also addressing the shortcoming which is a reduction in the in the power output or specific power output. Notice that this strategy does not require a higher mass flow rate of steam. The total mass flow rate of steam still remains the same 1 kg per second. However, the power is improved. So, specific power improves here not just net power, but specific power becomes better. So, the size of the equipment need not change. So, that is the advantage to reheat. So, we will redo the previous example with one reheat stage where the steam is heated to the same temperature as in the high pressure turbine entry. So, that means that state 3, temperature at state 3, T3 equal to T1 in this example. So, state 1 same as before, state 2 is also same as before because we use the same pressure for extracting the steam. Now, 2 is to 3 is heat addition. So, this is the reheat. So, this is the high pressure turbine. So, this is reheat and 4S to 5 is in the I am sorry 3 to 4S is the low pressure expansion in the low pressure turbine. So, this is at the condenser exit. So, this is a saturated liquid as before. This is compressed liquid state. So, I have not really given the details of how these property values have been worked out. I leave that as an exercise to you to work out. In fact, it is advisable in all the work examples for you to actually work out the problem by yourself and then check your answers. And wherever there are discrepancies, we can actually look at the procedure and then see where you have made a mistake. So, I strongly urge you to do that, pause the recording, work out the problem on your own and then come back and compare the answers. So, this is saturated liquid at the exit to the open feed water heater. So, this is compressed liquid at entry to the boiler. So, now we can repeat the calculation. So, heat supplied. Now, heat is supplied at two different locations. One, the feed water in the boiler, number one, number two, they are reheat steam in the boiler. So, these are the two places or parts in the cycle where heat is added. And you may recall that X was evaluated to be equal to 0.313 in the previous example. Let us just quickly go back and check that. So, X was worked out to be 0.313. So, the heat added now is 2728.44, much higher than before. So, without reheat, heat supplied was 2363. Now it is 2728. Heat rejected is 1447. Again, heat rejected is also more than before. Let us just quickly go back and check. So, heat rejected was 1284. Now it is 1447. And the work produced by the turbines, now we have HPT, high pressure turbine and low pressure turbine. So, the work produced by the turbine is 1298.7 kilojoule per kilogram compared to 1096 kilojoule per kilogram without reheat. Work supplied to the pump same as before because we are using the same open feed water heater. So, the net power generated is 1280.9 kilowatts per unit mass flow rate of steam which is higher than what we had before definitely. So, the thermal efficiency now as you can see is about 47 percent. And so, we have managed to retain the benefits of higher thermal efficiency. We will also check the second law efficiency, but the power output definitely is higher now compared to before as we expected. And not only is the power output more, notice that the specific power output has increased. This means that there is no change in the sizing of the equipment that is very important. So, we may calculate rate at which exergy is supplied to be 1770. Remember this QH dot includes the initial heat that is added to the feed water plus heat added in the reheat part of the cycle. The rate at which heat exergy is recovered comes out to be 1389 and the second law efficiency is 78.51 percentage. So, addition of reheat to the regeneration cycle has now addressed all the deficiencies in the cycle. So, we have a very good cycle now. Reheat with open or closed regenerative feed water heating. Now, second law efficiency still continues to be high even though we have another stage of heat because the temperature at entry to the boiler is quite high because of feed water heating. And the temperature at entry to the reheat section of the boiler is also high because state 2S is also at a reasonably high pressure. So, the exergy destruction due to heat transfer across a finite temperature difference in the boiler is less because the temperature at entry to the boiler both state 8S and state 2S are reasonably high. So, now if we compare all the results from all the variations that we have done so far in the cycle. So, the basic cycle had performance parameters like this thermal efficiency 38 percent, second law efficiency 81 percent. Remember these cycles are all operating between the same boiler pressure and the same condenser pressure it is very important. So, we are making a fair comparison and the degree of super heat in all these cycles is the same. So, addition of super heat improved the thermal efficiency, improved the specific work, but reduced the second law efficiency. So, let us show this in green to indicate that this is a good thing. So, this is a good thing it improved this it improved this, but reduced the second law efficiency. Now regenerative heating whether it is open or closed feed water resulted in thermal efficiency becoming higher. So, this was higher and the second law efficiency also improved because the rate of exergy destruction in the boiler was brought down. However, you can see that the specific power output decreased as a result of this. So, this came down and this was then addressed with reheat one stage of reheat. So, the one stage of reheat improved the overall thermal efficiency, it also improved the second law efficiency, it also improved the specific power output. In a typical thermal power plant it is customary to have 2 or 3 feed water heaters and between 2 and 3 reheat stages depending on the peak pressure and peak temperature in the cycle usually depending on the peak pressure in the cycle and that is what we will see now. So, what we want to see now is how well this translates to the real application which is actual power plant that are in use today. Let us take a look at that. So, here we are looking at 1 gigawatt thermal power station. So, as you can see this consumes 12000 tons of coal a day and about 98 million liters of water a day which actually would be the drinking water supply for a moderately sized city. So, it produces although it is rated 1000 megawatts the electrical power output is around 920 megawatts with 80 megawatts going back to the plant itself for other needs. Distressingly it produces 4200 tons of ash a day typical numbers and 30,000 tons a day of CO2 and 680 tons of socks and nox per day. What is the layout for this plant look like? So, you can see the boiler here and other arrangements. So, if you look at this you notice that there are 3 turbines instead of 2 that we had shown. We have a high pressure turbine, we have an intermediate pressure turbine and we have a low pressure turbine. And you can see the condenser which we looked at earlier. You can see you can look at one feed water heater and another feed water heater here. So, this uses 2 feed water heater. There is also an additional component here known as de aerator. Now, you may recall that we for all the examples that we worked out we said that the condenser was operating at a temperature of 45 degree Celsius. And you know very well that the saturation pressure corresponding to 100 degree Celsius is 100 kilopascal or atmospheric pressure. So, that means the saturation pressure corresponding to 45 degree Celsius is less than the ambient pressure. That means the condenser actually operates in a vacuum and that is shown here. So, the condenser actually operates in a vacuum which means that air if it leaks inside can actually get dissolved because of the high pressure. And that is not a good thing when we send the steam to the high pressure turbine or any of the other components because instead of having pure water it is going to have pure water plus dissolved gases which will affect the performance, adversely affect the performance of all these components turbine and so on. So, there is usually a component known as de aerator where we bring the pressure closer to atmospheric pressure and then let the dissolved gases come out and then the water is then circulated in the flow circuit. So, that is the purpose of the de aerator. We can also notice that the boiler has various sections. The economizer is an initial section which is used for raising the temperature of the water. And then we have what is a section of the boiler called evaporator where the liquid water the condenser pressure and temperature is converted to a vapor. This is then taken to a super heater here super heater section of the boiler and the super heated steam this we have marked as state one in our cycle diagram. This super heated steam is then taken to the high pressure turbine. So, after expansion from the high pressure turbine part of the steam is taken to as you can see here part of the steam is taken to the feed water heater and the rest is then taken to the reheat section of the boiler just as we explained. And the reheated steam is then taken to the intermediate pressure turbine. Notice that the intermediate pressure turbine has expansion going axially outwards from the middle. This is very beneficial from a mechanical balancing perspective because the net force on the turbine rotor is 0 because you have expansion taking place in opposite directions. So, balancing the turbine rotor becomes relatively easy. So, expansion takes place in this and then as you can see after the steam undergoes expansion in the intermediate pressure turbine it is then taken to the low pressure turbine where it undergoes further expansion. And part of the steam as you can see here is extracted from the low pressure turbine and sent to another. So, this is the blood steam which is then sent to another feed water heater. This is at a lower pressure. So, this design or layout utilizes two feed water heaters and three turbines. And you can also see that this is the feed water that comes from the low pressure turbine and cooling water is circulated separately in this circuit here. The cooling water does not mix with the condensate from the low pressure turbine because the condenser is operating in a vacuum. So, the cooling water is taken from the cooling tower. Usually it is taken from nearby river or pond or lake and it is used to cool the water in the condenser. So, this coolant is what is actually used to reduce the temperature, update the condensate from state 4S to state 5. So, the flow rate of the cooling water is adjusted so that the condensate which enters the condenser leaves as a saturated liquid. So, that is how the flow rate is adjusted and this water is then actually cooled back to ambient temperature. It gets heated up to temperatures perhaps around 45, 50 degree Celsius or so and it is then cooled in the cooling tower before being brought back. So, you can see that all the components that are shown in this layout of a practical 1 gigawatt thermal power plant correspond exactly with what we have seen so far including the pressures and temperatures. Notice that this condenser also operates at 45 degree Celsius and the pressures, temperatures are all very similar to what we have seen so far. So, whatever knowledge and understanding that you have gained from this discussion so far you should be able to use easily to analyze a power station like this, practical power station like this. The only component that we have not seen so far is the cooling tower and this is something that we will discuss in the module on psychrometry operation of the cooling tower and how the water management in the cooling tower is carried out to accomplish this purpose of cooling the condensate. And again once again let me emphasize that this was the main objective of the course to translate ideas that you learned in the first level course to practical applications and see what the practical difficulties are, difficulties in implementation. You can have any rank and cycle between any two pressures, any high temperature, but when you have certain performance, realistic performance parameters like specific power, first law efficiency, second law efficiency and you want an optimal design that gives optimal values for all these three parameters then many variations. So, here we started with the basic rank and cycle then we went through many variations each of each one of which accomplished a certain objective as you can see here. So, that is the primary objective of the course to take remember all the basic concepts that you need to know to do this analysis were developed earlier except for the notion of exergy and rate of exergy destruction and so on. All the other ideas were developed in the previous course applying you know steady flow energy equation to each one of the components calculating the thermal efficiency and so on. All these were learned earlier. Now, a modern power plant actually operates at pressures higher than critical pressure as I mentioned earlier. So, typical supercritical cycle diagram for a supercritical power plant would look like this. So, the condensate liquid condensate is pumped to a supercritical pressure and because this pressure and temperature. So, this has peak temperatures around 600 degree Celsius because this pressure and temperature is so high it is customary to have three turbines in this type of layout high pressure turbine and intermediate pressure turbine and a low pressure turbine with the different with multiple numbers of feed water heaters. So, supercritical power plant is one in which the boiler pressure is greater than 221 bar but less than 300 bar. So, 221 bar is the critical pressure of water greater than 221 but less than 300. Whereas, an ultra supercritical power plant which is what is being used which is current state of the art has pressures 300 bar or higher. So, one is limited only by the metallurgy of the boiler material because the thermal loads are very high this has utilization factors approaching 100 the thermal loads are very very high. So, only metallurgical limitations prevent us from increasing these values even more and typical efficiencies for supercritical would be around 50 percent and for this ultra supercritical it is around 55 percent. For a peak temperature of 600 and a condensate temperature of 45 degree Celsius you can work out the coronal efficiency and then see how well it compares with this. You will see that the these values of efficiency are not actually that far away from the coronal efficiency. So, we are actually operating at very very high efficiencies in thermal plants today with ultra supercritical technology. The next topic that we will take up is air standard cycle. Air standard cycle differs from both the Rankine cycle as well as the vapor compression cycle in certain important ways. We will discuss this and in the next lecture then consider three air standard cycles Brayton cycle, Otto cycle which is representative of a spark ignition internal combustion engine and diesel cycle which is representative of compression ignition diesel engine.