Welcome back. So what is the largest fuel source for Rankine power plants in the world. Now hopefully you went back and removed your notes from earlier. Coal is the single largest source of heat used in these steam or Rankine power plants. We also have nuclear as a means to produce heat, but coal is number one. And if we look at combustion in general, combustion of fossil fuels provides over 85% of the power in the world, for the stationary and the transportation sectors. So we're going to talk about those energy carriers later in the class. But we'll discuss the implications of using coal and some of the other renewable and proposed sustainable energy carriers. Okay. But let's get back to our Rankine power play. So last time we introduced the basic components. We talked about the ideal cycle which is the Carnot cycle, and then we introduced the real components in a in an actual Rankine steam power plant. And we're going to draw those again here, the components. And what we want to discuss now is before we talked about the pressure volume, specific volume diagram, and how those components perform on a PV diagram. Now what we want to do is map those components to a temperature entropy diagram. So again we're going to have to build this piece by piece. So let's start with the basics again. So remember the four components, the four introductory components, to my steam power plant, are my pump, where I'm going to take my low energy fluid, and I'm going to increase the energy of my fluid so I can pass that higher-pressure, higher-energy fluid through a boiler. And then, I'm going to take that high-energy fluid, and I'm going to expand it through my turbine. After I've extracted the work out of that turbine, I'm then going to condense the steam back to a liquid state. And that connects my cycle. And recall we called that state one. This is state two. This is state three. And this is state four. Exiting the pump. And here's my turbine. And recall we had work out of the turbine. We had work in to the pump. We add heat into the system at the boiler and we reject heat out of the power plant system at the condenser. So last time we looked at a pressure specific volume diagram. And we said first thing we always do is we like to draw our vapor dome. And because there are two heat exchangers, which are the boiler and the condensor, we know that we need to draw two isotherms which correspond to isobars when we're within the saturation region. And we said that the state one at the entrance to the turbine Would be a fully saturated vapor, and we would then expand from state 1 to state 2, and then condense to a saturated, for the Carnot cycle, we stopped somewhere within this pressure isobar within the saturation region. For my Rankine cycle, so this would be state 3 for Carnot, and we're going to revisit this in just a few moments. Comparing the Carnot cycle and Rankine cycle, but this is the exit state for my Rankine cycle. For the exit state of the Rankine cycle, we know we're going to take that to a fully saturated liquid, so we're going to put that right on the quality of X equals 0. On the pressure on the, low pressure line of a condenser. And then we're going to pump our fluid up to the pressure required for the entrance to the boiler. And that's going to be state 4. So this is the high pressure line in the system. Now thats the pressure volume diagram. Remember when we talked about this second lull. We introduced the concept of entropy and again we're going to recognize entropy is a thermodynamic parameter. It can be used to describe the state of a system, just like pressure and temperature and enthalpy and specific volume. We just haven't discussed the specific state relations, again, because those are a bit complicated, and we don't need them for this discussion. Instead, what we want to do, is we're going to introduce the temperature entropy diagram. And we're going to describe how these components perform. And their ideal behavior. So again, I'm putting my vapor dome on the temperature entropy diagram, and again we have a boiler and a condenser, so we have two isobars, two pressures, that exist in this system. And for temperature and entropy, isobars look like this. Now, we know within the dome They have to be constant because temperature and pressure within the dome are constant. Higher pressure of course corresponds to higher temperature when we're out in the vapor region. So we know this is P high, and we'll call this P low. Okay, and this condenser, this is associated with pressure P low. The boiler's associated with pressure P high. So, we're going to map these conditions from the P-V diagram onto our temperature entropy diagram. Well state one's pretty easy because that's a fully saturated vapor. So, you have the saturated vapor at state one. And here's the key piece of information we need to understand. For an ideal turbine, which is considered adiabatic and ideal. So adiabatic which we know what that means. Adiabatic means Q for the turbine is equal to zero. And ideal. This is a statement It's a mathematical statement about the second law. Which we don't have the equation form of it, but I can tell you that the outcome of this criteria. This adiabatic criteria, plus ideal performance, gives me And isenropic process. So one plus two means S is equal to a constant. Okay? So, something I'll keep rephrasing this cause this is really important. Adiabatic and ideal Processes are isentropic. And a process that's isentropic, just like a system that's isobaric means constant pressure, isentropic means constant entrophy. And again remember, that's designated as an S. And what we're saying is, there's no change in the entropy. So on this diagram, the expansion through the turbine is simple. An isentropic process is a constant, is a straight line, a straight vertical line on a T-S diagram. And then we're going to expand, again state three for the Rankine cycle. I'm going to drop the Rankine subscript. It's easy again, because we're going to pin that to saturated liquid. So here we have a saturated vapor, here we have a saturated liquid. A pump, just like a turbine, if it's ideal and adiabatic Is going to be isentropic. Okay. And again, because it's a power cycle, we know that all these processes are in clockwise movement. So one, two, three, four. We have a clockwise movement. And here's state four. And you can see why we like the temperature entropy diagram for these. Power cycles, because they're sort of a box and we're gon, again, we're going to come back to that. The only part that isn't a rectangle is this little portion right here, prior to the entrance of the boiler where we're a little bit outside the vapor dome. Okay, so you should be able to draw both these diagrams of the pressure vapor and the temperature entropy diagram for these basic components. And we'll start taking this basic layout and we're going to perturb it, we're going to look at a number of different ways we can change it. We're going to look at how does a non ideal system behave, so where are the losses that we would see in the system. And we're also going to look at how can I make the power plant better? How can I improve the work out of it and how can I improve the thermodynamic efficiency? And we're going to start with this temperature entropy diagram. Okay, and the reason for that is the second law again, and we talked about this conceptually, describes maximum performance, and minimum required work. So, if we had introduced the second law equations, we could actually show you why the temperature entropy diagram is the best place for us to benchmark ideal performance. Okay, so, let's compare the Rankine and the Carnot power cycles. Again, on this temperature entropy coordinate space. So again, always start with your vapor dome. And if it's temperature and entropy, make sure you draw your isobars. And again, for as many heat exchangers as you have in the system, you should draw your isobar. So here's P high. Here's P low. So I'm just going to repeat the figure we had before. So here's state one, here's state two. Again, constant entropy expansion, oops, sorry. This is state three. And here's state four. Okay. Now that's the A processes, the four processes for the Rankine cycle. Now recall the Carnot cycle, let's go ahead and change colors here just to emphasize that, so remember Carnot is the best we're ever going to do with our heat engine. So the Carnot remember told us the maximum performance for the cycle. So the Carnot efficiency remember is max. Carnot, this is redundant, but it's always good for us to emphasize our important characteristics. So the Carnot cycle was defined some maximum performance out of our power cycle and it's completely defined by the temperatures. Of the high temperature reservoir and the low temperature reservoir so there's Carnot and remember the Carnot cycle had our 4 steps so 1 to 2 was isentropic expansion and then 2 to 3 was constant temperature or isothermal. Heat rejection, three to four was isentropic compression. And then four to one to complete that loop in the cycle was constant temperature heat addition. Okay. So let's come back over here to our TS diagram. Now the red is for the Rankine, the blue is going to be for the Carnot. So let's start with the same, initial state. I'll circle that so we know that the Carnot. Carnot here is shown in blue. It's going to start from the same initial state that we have for the Rankine cycle. And now we're going to isotropically expand, and that looks identical. So enough it does. And then we have constant temperature heat rejection, that's from 2 to 3. Well, Conveniently or maybe smartly creatively however we want to rephrase it from 2 to 3 because there's phase change and I'm at a constant pressure in other words I'm at a constant pressure within the dull then that means I'm also at a constant temperature. So the heat rejection for the Rankine cycle is constant temperature heat rejection, at least with the way I've shown it in this sketch. Okay, the catch is that the Rankine cycle goes all the way to the end here, but the Carnot cycle is going to stop. Remember we talked about this before, so my Carnot cycle is going to stop here, so this is three Carnot. This is 3 Rankine and I'll change colors again but we'll go add the R here so we understand that's the Rankine. And we'll now get rid of this blue net that's confusing. So the Carnot cycle actually doesn't continue to the saturated liquid state it stops here. It has to stop here, because I need to do a constant temperature for a fair comparison. For me to make this apples to apples, the Carnot cycle has to stop here, while it's still a constant-temperature process, and it's still within the dome. And then I have my isentropic compression. So this would be 4 Carnot. Okay. And then, we close the loop, we close the cycle by returning to state 1. So again, the blue is the Carnot cycle, and the red is the Rankine cycle. So let's go back here. [SOUND] And so we look at the Carnot cycle efficiency and it's defined by this T low and T high, and we can see very clearly where the Carnot T low and T high are defined in our process diagram here. Right. Here's T high. And here's T low. For the Rankine cycle I'll tell you if we invoke the second law, and I'm just going to provide you with this formula. And if you want to you can follow up with some nice resources, in the reading material that describe how to make this approximation. But I'm just going to state that if we invoke some of our second law an, analysis, what we would find is that the Rankine cycle can be approximated using a formula that looks about the same as this Carnot formula. But there's a key difference, and I'll show you what that is. The Rankine cycle can be approximated by 1 minus T out, just like it was before, T low, here, so T low, divided by an average temperature that is the average temperature for the heat addition. And that average temperature's going to be this temperature. The temperature average from state four all the way to state one. So you can see the Carnot cycle this tn here, this t high. Okay, this is T high, is going to to a higher value than the Rankine cycle. Right, the Rankine has this little piece right here. Which is at a lower temperature than the Carnot cycle, so that is a slightly lower efficiency than the Carnot cycle. Okay. But we can look at the features of both the Rankine efficiency and the Carnot efficiency, and we can make some pretty general conclusions, which are the same conclusions we made when we discussed this for Carnot. Which is you generally want the low temperature to be as low as possible and the high temperature to be as high as possible. So, to increase the efficiency, and it doesn't matter if its Rankine or Carnot, thats what this is telling us. That hey, the strategies to improve Carnot performance are the same strategies to improve Rankine performance. So to increase the cycle efficiency we want to increase T high and to decrease T low. Okay or T out and T in T high is T in and T low is T out. OK, so, we look at our Rankine diagram, we say, how can I increase T High? Well, increasing the high-temperature process is the same thing as increasing the pressure when you're in the dome. So what we want to do is increase the temperature of the boiler. By increasing the pressure of the boiler. So we say that as, want to increase T high, which is the temperature of the boiler, and that's the same thing as saying, therefore, want, we want to Increase the temperature of the boiler. Okay. Conversely we want to decrease the temperature of the condense, so. And these are really good practical operating strategies. To improve the performance of the cycle efficiency of our Rankine or Carnot cycle, we want to do the same thing. We want to spread those two temperatures as far apart as possible, which it really is saying, spread the operating pressures of those two processes as far apart as possible. Okay. So, we have strategy for how to imporove the thermal efficiency of the power plant. We've already said those 2 key things. We want to increase P, the pressure operating pressure of the boiler, and we want to decrease the operating pressure of the condenser. Okay. As you increase the operating pressure of the boiler, you're going to increase the temperature, which is what we're trying to do from the thermodynamic analysis standpoint. So what limits you? I want you to think about, these are 2 questions I want you to think about. There are practical limits associated with increasing the pressure of the boiler. And decreasing the pressure of the condenser. One is a little bit more intuitive than the other. So what I want you to think about before you come back is what's the practical lower limit for the low pressure operating condition of a power plant. And we'll discuss that when we get back.
