Welcome back. So, the practical lower limit for a power plant is somewhat intuitive. We don't want to go below ambient pressure, because then we risk having air or other contaminants leak into the system. And then, we would have to increase the quality of the connections. We'd have to have leak tight parts, and vacuum has costs associated with it. So, vacuum being anything below the ambient pressure. So, in general, we want to stay right about ambient pressure. In terms of our lower limit. So, that really defines our lower temperature too. So if our, if we're going to operate the condenser at let's say ambient pressure, then our heat rejection temperature is going to be about ambient temperatures. And again, that's linked to how are we going to cool the condenser. And typically we're going to, it might be a little better than ambient air temperatures, because we can use water as in our heat exchanger. In order to keep those temperatures, let's say more like 50 degrees Fahrenheit, if we're using like a large water as a reservoir to cool in the condenser side. So again, for the lower limit, it's kind of intuitive. The upper limit p high is little less intuitive, and you might have to have some expertise with turbo machinery and boilers. What we will bump into are materials constraints. So, as we increase the pressure in the boiler, we're going to have a higher temperature entering the turbine. And what we are typically constrained by right now are the material properties associated with the turbine. So, the turbine has a maximum inlet temperature that it can handle. And we'll talk about that more in our strategies for improving the performance of our power plant, which is what we'll talk about in just a couple of slides. Okay, so real power cycles. Where are the losses? So, I promised you we'd actually talk about those losses in an actual system. And again, we'll start with our temperature entropy diagram as a means to have that conversation. So, here's my vapor dome like before. Let's draw my basic power cycle, in ideal performance. So, we'll put our two isobars on here. Okay. So, we have the entrance to the turbine the exit of the boiler. We expand across the turbine. There's two. Exit of the condenser remember is a saturated liquid. We compressed through the pump, and that completes my cycle. So, with heat exchangers, remember the two heat exchangers are here, so here's Q in, and here's Q out. And remember this is the condenser, and this is the boiler. And the primary way that we're going to see a loss on the boiler of the condenser is in the form of drop of pressure. So, we're going to lose some of that pressure at the high pressure condition. So, if we were to drop the actual process here, it might be something more like this. So, this would be one, the exit of the boiler with losses, and this is what they call pressure head. So, we'll lose some of the operating pressure associated with the boiler. With the turbine, this is the ideal performance of the turbine. Remember, we said it's adiabatic and isotropic. Those are the two criteria for the ideal turbine. A real turbine is non-isentropic. So, this is the exit state of the boiler with losses. Real turbines and real pumps are non-isentropic. And in fact, second law states we have to increase entropy generation with each of those steps, which is going to tell us that we have to have an exit state that's in fact, the actual state is here. So then, we'll call this 2actual. Okay, for the turbine. And this would be two isentropic. And what we would do is compare the device performance, we will circle back to this, but it's going to take us a little bit of time to get there. We talked about ideal cycle performance and how we used the Carnot Cycle to define that. Devise performance is also defined by the second law, as we mentioned in the last couple segments ago. And what we would do is compare the work out of these two processes. The isentropic process and then the actual process. And we would define that as the device efficiency. And again, just so you have a reference and some foreshadow for where we're going. Turbines are typically 80, 90% efficient, they're pretty in terms of the isentropic efficiencies, they're pretty decent. You know, if you have a lower performer, it might be in the 70 percentile. Okay, so, but we're going to constrain the system that it still has to meet the pressure that we were targeting for the condenser. The exit state of the turbine still has to get that exit pressure. The entrance pressure to the condenser. Or the exit pressure at the turbine. And then, again in a heat exchanger, we'll indicate our losses as being pressure losses, so it would look something like this. Okay. And nominally, you're not going to lose pressure below the ambient, right? Because at that point you're going to potentially have your system. You would have ambient pressure, ambient gases potentially leak into the system. So, this probably limited by the ambient pressure, so you'd run your condenser at slightly above the atmospheric conditions. Okay. And then, again, we're going to target that the exit condition has to be a fully saturated liquid. And in the case of the pump, non ideal performance is actually going to move it like this. So, this is the actual exit condition. Again, I'm going to aim for the boiler's ideal pressure. And this is the isentropic exit condition. So, again, the, the losses are for each component. And the way we describe those component losses depends on the type of function that we have. So, for turbines and pumps, they're non-isentropic. For real boilers and condensers, are non-isobaric. Now for the domain of heat exchangers condensers and boilers as the name implies is dominated by heat transfer. So, heat transfer systems have some very sophisticated ways of characterizing performance. So, for pumps and turbines we're going to use efficiencies. So, we will define a turbine efficiency and pump efficiencies. For these heat exchangers, we define effectiveness. And so, that's usually denoted as a Greek letter e and that's, again, effectiveness for heat exchangers. Now, that's very sophisticated. It's a whole science in and of itself. And so, we won't cover the details of how you define effectiveness. Again, just like for the turbine and pump efficiencies, I'll give you an efficiency and you should know how to determine from an ideal efficiency, what's the actual work from a turbine. What's the actual work required by a pump. Similarly, if I give you the effectiveness, you should be able to determine the actual heat transfer into the boiler or out of the condenser. Defining the effeciencies for the turbine and the pump, and defining the effectiveness for the heat exchangers is not going to be covered in this class. But it's a pretty straight forward science that's based on everything you learned here. So, it's a natural next step for what you might want to study next on these systems. So again, effectiveness defines performance of heat exchangers. And always remember your boilers and condensers are phase-change heat exchangers. Which so boilers and condensers. So, we will circle back to these topics, of like how we, put all of our little steps, all of our processes together. But we're going to build a little bit more before we come back to that. because what I'm going to tell you right now, is everything that we just learned about the basic Rankine power plant is pretty much basic entry level. And no one would operate a plant at those conditions. So, in fact, the power plants are much more sophisticated than we showed in our basic cycle. And you might have already guessed that. But the very first thing we're going to do is improve the cycle efficiency by adding what we call super heaters. And those have very significant practical performance issues. They also improve the cycle efficiency and we'll be able to see that through our basic equations and through just sketching the cycle on our temperature attribute diagram. So, that's what we're going to do now. Okay. So, we take our basic power plant cycle. So, we have our pump. We have our condenser, and we have our turbine. And up here, we have our boiler. Notice, I'm making our boiler much stubbier than it was before because what I want to do is emphasize here our superheater. So, what we're going to do is take, let's label our system, so here's my pump. Here's my turbine, here's my condenser, here's my boiler. Okay, on my basic temperature entropy diagram. We had one, two, three, four, and again, where we said this is going to be the entrance state to the turbine. Well, there are a couple of key issues we haven't discussed. One is, your turbine doesn't like multi-phase materials. So, notice that is we had a saturated vapor here, and we put that into the turbine, and expand that liquid, or expand that fluid across the turbine, what we see as we come down here, is we're going to have a fluid that's actually a multi-phase fluid. It's going to have some aspects of vapor, and some aspects of liquid. And for this turbo machinery that's rotating, those droplets are going to lead to a lot of durability issues. Pitting, so, potentially causing some significant damage to the turbine. So, we don't want to operate our turbine in a multi-phase mode. We want it to be entirely one phase, and entirely in the gas phase. So, from a practical standpoint, we don't want to operate here. From a practical standpoint, we want to move into this superheat region. Now, remember what we talked about last time. For my Rankine cycle, I said we could approximate the system. Approximate the cycle efficiency as being 1 minus the temperature which we reject heat. Divided by the average temperature that we add heat. So, I want to operate out here in the superheat region. Because it's better for the durability of my turbine. And if we look at this number here, here's T in average. Is defined by these limits here for the basic Rankine power plant. If I take that power plant, and say, I want to move this exit state out here, let's call that one superheat. Okay and this is just one boiler, with just the boiler. I'm going to address two issues simultaneously. I'm going to get that turbine so that it's only operating on a vapor, and I'm going to increase the temperature which I'm adding heat. So, we can see that here. So again, I'm going to isentropically expand through my turbine. So now, this is two, the exit state of the superheated steam. And you can see T in for this range of temperatures is significantly higher than we had for our basic Rankine power plant. So, let me show you that here. So, this is the average temperature, is averaged across this temperature domain, as opposed to this temperature domain for the basic boiler, basic system. So, we can go ahead and we'll add some annotation here to say, that's just for the boiler. I'm going to put my temperature axis back on there. And we can see that T in for the superheater, the average T in, is greater than the average temperature which we add heat for the basic boiler system. So, the Rankine cycle with super heat, that efficiency is greater than the Rankine cycle with just the boiler. What's the superheater? It's just another heat exchanger. And it's just a heat exchanger that's primarily, in general, they're not segmented like this right, we're not going to divide them. So, you would actually have the boiler and the super heater combined together and it's going to take us to this exit condition that's a super heated condition. So, every steam power plant has superheatering in it. It's a basic means to improve the cycle efficiency and to improve the performance of the overall system. And you can see just our simple discussion of the cycle efficiency tells you how to improve the performance of the power plant. Okay. But there are other technique too, including re-heaters. So re-heaters, say, are based on the exact same principle of superheaters. If I increase the average temperature which I add heat, I can increase the cycle efficiency, and the workout of my cycle. So, I start with our superheater. And now, we're going to add a re-heater. Okay. So, let's see where that re-heater sits within our cycle. So again, we have our pump. Now, we're going to go through our boiler plus superheater, our combined heat exchanger. And we're going to expand that high energy fluid through a turbine. And then, we're going to take that fluid, and we're going to add more heat. And that's our re-heater through another heat exchanger. So, there's my re-heater. And then, continue the expansion process through a second turbine. So, this is turbine 1. And this is turbine 2. And then, we're going to go through my condenser, and then connect back to my pump. So pump, condenser. Okay, the re-heater is a heat exchanger, so when you look at these cycles and you want to map them onto your cycle diagram. So again, we start with temperature and entropy. We need to count heat exchangers, and these are three distinct heat exchangers. Now the boiler and super heater again is a combined heat exchanger. So, for each heat exchanger I have one isobar that I need to sketch on my system. So, we have P high, P middle, P medium if you'd prefer, and P low. So, my superheater again is going to take that fluid and put it well into the superheat region. I'm going to expand through turbine 1 until I reach, let me go ahead and give you some state labels here. So, we're going to call this state one, again, just like it was before, the entrance to the turbine. Here's the exit of the turbine, so that's state 2. I'm then going to add heat in through this second heat exchanger. And that's going to take this fluid along the isobar to some higher temperature condition. And, often, what people will do is constrain the system so that it has the same exit temperature as we had for the initial state. So, often, we'll take it all the way up to here. But just to make sure you're not always constrained by that limit, I'm going to draw it here. So here's the exit state of the first re-heater. And then, we're going to isentropically expand outta the second turbine, that's going to take us to state four. Condense again to a liquid base. And then we're going to isentropically pump the fluid to a higher energy state. And here, you need to be careful going past that middle pressure, because remember, we have to be at the entrance to the boiler and superheater, which is on the highest isobar in the system. So, that's going to be state 6, and state 6, here. Okay, so what we see is, we have heat transfer that occurs here. And that's heat transfer 2. And then, we have heat transfer that occurs here. That's heat transfer 1. And so, if we go through the cycle analysis, we'll find that again, we're increasing the average temperature of the heat addition. And we're improving the cycle performance. You also need to recognize that we now have multiple heat additions to the cycle. We would analyze these the same way we set up the equations before. So, you would just have 2 heat in to the system. Just need to remember that. That your heat transfer for the cycle. Your net heat transfer for the cycle includes Q in 1 plus Q in 2, plus Q out. Now remember this is a negative number has a T transfer out. So, you just have to be careful in your accounting when we do the analysis of the systems that have more complex heat exchanges. Now, I drew this as a system that occurs in series so that we could see it very, very clearly. In reality there aren't two turbines, there are stage turbines. So, this would actually be a two stage turbine where we're withdrawing some fluid to go through the re-heater, and then it expands through the second stage of the turbine. Okay, so, again, this is drawn for simplicity. In reality, there aren't these distinct components. They're very much more compact. If this is a means to improve the performance on the high temperature engine, end of the cycle, we can do the parallel on the low temperature end. And so, we can add inner coolers. So, there are all these strategies for adding components and packaging them in different ways in order for us to improve the cycle performance and improve the work out of the turbine. We're not going to go through all those permutations and combinations. I can tell you that again, we're not even at the most basic form for a power cycle. Most of them will have multiple stages of turbine expansion, multiple re-heaters. they'll also do co-generation which is where we split mass transfer, we'll split fluid lines out of different stages out of different portions of the cycle. And it's all an optimization process. So, real power plants are much more complex, but the drivers for those complexities are the very basic thermodynamic equations that we've already covered. Based on enthalpy, comparing against Carnot efficiencies. Okay, so I think that's enough for what we want to cover in the Rankine power plants. what I want to do next is, again, they can get much more complicated and if you work in this area you know that firsthand. But what I want to do is show you how we can improve performance much more dramatically. It's kind of cheating, but not really and we'll show you how to do that in the next segment. what I want to leave you with right now is we've talked about the steam power cycle, that's the Rankine power cycle. The working fluid is water. Why do we use water as the working fluid for the Rankine power plant? So, you think this of this mathematically in terms of the equations we have developed, or you can consider this question conceptually. And that's what we'll start with next time.
