Okay, we were talking about the phase of the working fluid in the power plant. Would it matter if we used something that had phase change- water? Or would it matter if we used something that doesn't undergo phase change like air? Which will give us a higher theoretical efficiency? Well, in principle, it doesn't matter. Remember the limits on the power plant are defined by the temperature of the thermal reservoirs. In practice, it really does matter, and we want that phase change because it does give us a pretty good boost in terms of the energy. So that was sort of a trick question. Again, theory says it doesn't matter. Practice says well I can reach different temperatures, and I can do different things with the different working fluids. So we'll see exactly how as we go through the next few examples. Okay, so, we're going to go to the Rankine power plant first. This is also known as a steam power cycle. it's also called a vapor cycle, so you also hear a lot of different names. The Rankine cycle is the workhouse for over 80% of the power generation in the world. This is what we use, whether not it's a nuclear power plant, a solar power plant, a a coal-fired or natural gas. Now I'm going to put a little asterisk on that solar power plant, because it does sort of matter whether or not we're using a solar power in terms of a heat source. So, if it's a heat source, we typically use a ranking power plant. Now, if we're doing photo electrics, then we don't have a heat engine on our hands. And we'll be talking about that as we get to the, end of this class. We will discuss the different energy carriers and the pros and the cons. And that's important for us because now we know, if it's a heat engine for power generation, it's limited by the Carnot efficiency. Some of those power generation schemes are not heat engines and they're not limited by the Canot efficiency. Okay, so let's get back to task. Let's talk about the ranking power plant. Again, the work horse of where we generate, or how we generate stationary power around the world. So, we're called the general features. And these are the same as the general features that we had for the Carnot cycle. Where we have essentially a pump, [SOUND] a boiler, [SOUND], a turbine, [SOUND], and a condenser [SOUND]. And if you have an opportunity to tour a power plant often universities, schools, local district will have a power plant. You might be able to sign up for a public tour. They are fascinating to see and I would encourage you to take a look at some of those facilities. These boilers for example, are here at the University of Michigan, and we have a power plant on our campus that's a very forward thinking power plant. It's actually what we call a co-generation power plant, which we will discuss in just a couple of segments. and it actually can be transitioned from using relatively dirty fuels, dirty carbon based fossil fuels to a more clean natural gas based fuels. But the boiler at the University of Michigan Power Plant is about two or three stories high. So these are huge facilities, and what they are is essentially allot like your ovens you have a really big box. Very well insulated, and we have a serpentine of steam tubes, or pipes, that run through the boiler in order to heat the steam, that is, the working fluid. So again, this is steam, and that's another way of saying, our working fluid is water. Okay, and again, this heat transfer source can be a number of different sources. Natural gas is one of the cleanest burning fossil fuels, and so that seems to be the big movement in using natural gas. The catch is, globally, we have a lot of coal resources, and so coal is used often because it's inexpensive. Natural gas is becoming more and more inexpensive, at least in the United States, but coal is often less expensive around the world. So coal, which is a dirtier fuel, particularly if it's fired in a pulverized form, is the dominant source of power generation for the electric power sector. Okay, so then we have our turbine, and again we're going to spin the shaft, and we're going to take that, we're going to connect that shaft to an electric generator. And that's going to generate power out of my turbine. I have my pump, I'm going to need work into my pump. And of course the condenser down here is where we're going to reject heat. Okay, so every power plant has to have a physical medium where you can reject the heat. Often those are cooling ponds, so the body of water has to be sufficiently large. That you don't change the temperature of the heat source that you're rejecting, rejecting this heat to. So you have to have some pretty significant volume of water that you can reject the heat from the power plant. We won't go into the details in this class, but I would encourage you to explore. Sighting of power plants and actual power plants themselves are huge water hogs. They need water both for the operating fluid, and as make up water that's necessary to add. And again, typically we use a reservoir in order to reject heat. And of course, if you're talking about a system that's far from the ocean, you're using a fresh water reservoir. So there's a lot of competition between fresh water, relatively clean water that could be used for agricultural or societal purposes, drinking water. And for power generations. So that's a very large concern and how to reduce water use in power cycles, is a huge area of research and interest right now. Okay, so this again, this portion requires that we have some sort of cooling pond or some cooling lake. Notice that at all times I've considered this a closed loop system. So we're not at the point where we would consider, including makeup errors. So this is entirely closed. The working fluid does not leave, this system. So this cooling pond, what we have is essentially a heat exchanger down here with this working fluid does not mix with the fluid in the cooling pond. So I want to make sure that, that's clear. Again, this heat source, and the nuclear reactor, combustion of fossil fuels, or renewables. [SOUND]. So again boilers and condensers are heat exchangers. Cool, so we already went through the, our analysis of how do we, what are the simplifying assumptions associated with heat exchangers. And the entire thing is considered a closed loop. So, before, when we were drawing our system diagram, remember we had this was what's inside the box for our generic power cycle. If we drew this control surface here, this is a closed system, however, if I consider the components individually. So lets say I just consider the pump, this is an open system. Okay, so this just is a great example to emphasize to you, it's important that you define the system well. So if you want to treat the system as a closed system, you need to consider all of the components together. If you want to understand the specific pump work required, for example, you can only identify the pump work if you look at that specific component. If you looked at the entire system, the mass transfer doesn't cross the system boundaries. And you wouldn't be able to determine the flow rate for the pump, things like that. Okay, for this entire system, whether or not it's ideal, we are going to neglect kinetic and potential energy changes. Because as we already saw in our example, the energy mechanism. The energy transfer mechanisms that matters most in this system are the enthalpies associated with the flow system. The kinetic and potential energy effects are really small relative to the energy carrier or the working fluid itself. We're going to assume everything steady state, and steady flow. [SOUND]. And lastly we're going to assume no heat transfer with the surroundings, so the only and let me be very specific here. The heat transfer that occurs between the high temperature low temperature reservoirs, are not with the surroundings. So specifically what I'm saying is that, the pumps, and the turbines, are adiabatic. And that the boiler and condenser, only exchange heat, with the cooling lake, and with the reactor, the boiler, the, combustion furnace, okay. So, no heat transfer with ambient surroundings. [SOUND]. Okay, so these are the same assumptions that I would make, regardless of whether or not the system was I, ideal system or a Carnot system. Or whether it was an actual system like our Rankine power plant. Okay, so there are my general features. The next step is now to apply what we know about these different pieces of equipment and what we know about the conservation of energy. Okay, so let's do our basic analysis. So I'm going to write down again the most generic form of a conservation of mass. We're going to analyze each component one by one. So these are all controlled volumes. So the appropriate statement for the conservation of mass is the controlled volume form. [SOUND]. Okay, but pick any component. Let's just start with the turbine, because again, that's our workout, so that's our big power producer in this system. So, if we consider the turbine. And we go ahead and we apply our substance at its a steady state steady flow system. So this is going to be equal to zero we see that there's just one mass flow rate in and one mass flow rate out. And so the entire cycle or the entire power plant Is actually defined by one mass flow rate for our system. So, that's the simplification for the conservation of mass. So now, again, write the most generic form for the conservation of energy for a controlled volume. And we have are energy within the control volume, the transient term, the heat transfer, net heat transfer, network transfer. Plus the energy that's carried by the flow in the form of enthalpy, kinetic energy and potential energy, into the system. Into the system, and out of the system. Again, we've stated we're going to neglect the kinetic and potential energy effects as being small. [SOUND]. And now if we consider again the turbine, again, it's steady state. So that's going to be equal to zero, and we've already assumed that our turbine is essentially adiabatic. No heat transfer with the system. We get again the same expression we had when we did our previous example for the turbine. Which simply says, the work out of the turbine, the power out of the turbine normalized by the mass flow rate for the system. Is simply given by the difference in the enthalpy into and out of the turbine. So, we know that the pump is going to follow the exact same analytical procedure, so let's go ahead and just right that down, a priority. Where we have the work transfer for the pump, normalized by the mass transfer, is going to be given, by again, the difference between the entrance state and the exit state. We know for the turbine that this number will be greater than zero. We know for the pump that that number will be less than zero, because we need work transfer, into the system. Okay, so now let's consider the condenser, the condenser and the boiler. Let's do the condenser first, and we're just going to go ahead and in a different color. We'll simplify the conservation of energy equation we've already written down. Now remember, for the condenser, so this is, let me go ahead and label everybody here. This is our Turbine, this is our Pump. And now we're going to derive the appropriate conservation of energy for the Condenser, and then here's the Boiler. Okay, so, for the condenser we have a system, which is again, steady state, so this is, I'll label this as my condenser. We have to have heat transfer. That's already labeled on our previous diagram on our previous slide, and that 's the purpose, the function of the condenser is actually to reject heat. But it's a fixed volume system, and there's no shafts or anything, no electricity. Nothing moving in or out of a heat exchanger. So, instead of having an adiabatic turbine, what we have is a no work or no power transfer associated with the condenser. So this is equal to 0, so we'll put no shafts electrical work, etcetera. Again, we'll neglect the changes in kinetic and potential energy. And all we're left with is essentially that the heat transfer has to be balanced by the enthalpy transfer. So we have an expression that looks like this for the condenser. So Q, I'll call it condenser which is also Q out. Again I hope you're very flexible and understanding how to label these and which one works best for you. But condenser, out, cold, however you want to label it, this is the heat rejected from the power cycle. Has to be balanced by h, the enthalpy at state 3, minus the enthalpy at state 2. Okay, and the boiler is going to have exactly the same form. So, this is the boiler, again, normalized by the mass flow rate. And this is going to be the heat transfer; the high temperature of the heat in. So this is also, we've labeled them a number of different things, but they all work. [SOUND]. And for the boiler the difference in states is h1 minus h4. So again, let's just flip back to the previous slide so we can remember, that's 1, 2, 3, 4. So state one is the high energy state that enters the turbine. So let's go back to our slide for the analysis here. So, again, this is the high energy state, h1, minus h4, that's the low energy state. So that means this number at the exit of the boiler for enthalpy is higher than the number at the entrance, so this number is greater than 0. That's positive, and it's heat in. Which is consistent with what we would expect. You can apply the same argument to the condenser, which tells you that's going to be less than zero. And that's going to be heat out, okay? So now we have the basic analysis. Those are the four components, we've got governing equations for. The conservation of energy for each one. Now we can put it together and look at the overall efficiency or performance for the steam power cycle. Okay, so the overall thermal efficiency, remember for any power plant, is defined by the work out of the cycle. Divided by what we paid for to get it which was the heat transfer into the cycle. And again, we're doing this on a rate basis since that's the form that all of our equations are given on. The work for the network for the cycle we need to remember includes the work that is developed, or generated, by the turbine. I'm going to go ahead and put a positive sign here right now and I'll explain that. Plus the word required by the pump. The way we wrote our equation for the pump analysis, this number will be negative. I don't want to put a negative sign here, okay? And then we have the heat transfer in, and we can take each of these and normalized the numerator and the denominator by the mass flow rate. And then we can go ahead and substitute in the expressions that we just arrived in the previous slide. And what we have is now an expression for the power plant efficiency, which said [SOUND] like this. And we could do, we could shuffle things around a bit and do some Algebra and make it a little prettier, but not much prettier, and we'll get this expression. [SOUND]. For the power plant efficiency. So when you ever hear somebody talking about the efficiency of a power plant, this is the efficiency that they're talking about. The thermal efficiency of the power plant. And as you, some would expect for an actual power plant, the efficiency depends on the state at all four key conditions. So at all four states. The entrance and exits of all of the individual components. The Carnot efficiency, only cares about the two temperatures in the system. The actual efficiencies includes contributions from each of the states. Whether or not the components are ideal or non-ideal doesn't matter to this equation. I can have an ideal turbine, I can have an ideal pump. I can have a real condenser I can have a real boiler this expression doesn't change. Okay, the entire thermodynamic efficiency is defined by the enthalpies of the components. The enthalpies of the states for the components. now we're going to pause. We'll come back to this analysis in just a moment, and what we're going to do is use this analysis to show us how can we make our power plants better. And the key metric here is the thermal efficiency. Okay, what's the largest fuel source for Rankine power plants in the world? Go ahead and check your first segment notes if you can't remember. We've talked about it since then, so I hope you will remember, but come back with that answer next time, and we'll talk about that.
