[BLANK_AUDIO]. Welcome back. So, last time, we talked about a way that we can improve the efficiency out of our power plant. It was a little bit of a cheat. Because what we did was redefined the efficiency to include heat transfer as a desirable output of our power plant. And we called those plants co-generation plants, or combined heat and power plants. So with those power plants, we had a couple of issues that we had to consider. One is, of course, the desired power output out of the plant. And what we're going to do with the heat transfer. So I gave you an example of a system where we generated both power and heat that was used for sterilization purposes. So what are some of the issues that you want to consider if you're going to build a CHP plant? One is, very important, heat transfer cannot be efficiently moved very far. Distances will decrease the efficiency of the heat transfer. And you have to decide whether or not you're going to meet he electrical needs or the heat transfer needs. It's very unlikely that you're going to be able to hit both targets simultaneously and we'll do an example a little later that will show you exactly what I mean by why we struggle with trying to hit two targets simultaneously. Okay, what I want to talk about next is air standard power cycles, so last time or for the past unit we've been discussing Rankine power cycles which are steam power cycles, which use water as the working fluid. And that's what the majority of the power plants around the world are based on, but there are also air standard power cycles. These cycles are the basis for jet engines, and also for some stationary power as well. They're becoming a bigger and bigger part of the stationary power sector because this is a basis for natural gas fired turbines. Okay, so we're going to go through these pretty briefly because we already know how all the components work. So the air standard power cycle looks a lot like the Rankine cycle. Here we have a compressor, a burner this is a heat exchanger just like we had before and then we're going to expand that high energy fluid out through the turbine. And then we're going to exhaust that combustion gases which are mostly hot air Out the stack, the power plant, or out the back of a jet engine in that case. Now remember for this to be a cycle, the cycle has to begin where it ends. So when we analyze this system, typically what we do is we put a fictional heat exchanger here. Doesn't really exist, but that that would allow us To complete the cycles, so we have a true cycle where we begin, where we end. So again this burner up here is refereed to as a combustor but it's again a heat exchanger. Now these are air standard power cycles, so when we burn fuels like natural gas. The working fluid is actually the combustion gases and air. And if we go through some pretty advanced thermodynamics, what we find out is that the combustion gases like natural gas. Make up a very small portion of the overall working fluid. So we generally assume the working fluid is just air. Okay, so that's why they're called air standard power cycles, so it's important for us to remember the working fluid is air, and as you might anticipate we're going to use the ideal gas law for our analysis... The ideal gas model. But the component analysis, before we apply the assumptions or the model of the ideal gas, are going to look exactly like they did for the rankine cycle. So let's take, instead of a compressor we have a pump, but the function is the same which is to take. A low energy fluid at state one and move that to a higher energy fluid at state two. The heat exchangers have the same ideal assumptions, which is that they're isobaric from entrance to exit. And the compressor and the turbine, again, if we assume that they're ideal with no losses, are also going to be isotropic, and that's what we see on our temperature entropy diagram here. But because the working fluid is air, notice there's no saturation region, right? We're not going to have any phase change in this system. If we were to draw the saturation region, it'd be somewhere down here, right? It'd be off the scale. So for air, as we go through the compressor, it's isotropic from one to two. We have a constant pressure line. And this is going to be that high pressure, right, because this is the burner, the combuster. So from two to three, we have constant pressure heat addition, so that's going to be the Qn. And this heat transfer occurs by combustion. So, like we had with our coal-fired power plant, we had heat transfer by combustion, in this case we're going to use natural gas or propane or some other fuel. We're also going to have heat transfer that occurs at constant pressure. So from 2 to 3, that's my heat into the cycle. From 3 to 4, I'm going to expand through the turbine. That's where I'm going to generate the power out of the cycle. And then, to close the loop, I have this fictional heat exchanger from 4 to 1. And hopefully, you see what I mean by, if we feed air into the system. And then we exhausted out the stacks. We don't really have a physical heat exchanger in this cycle. Alright. This is, image your jet engine on an airplane. You essentially have the inlet, which then compresses the air, you have the combusted which adds fuel and we burn the air, and then you have the expansion out the back of the jet engine, but there's no heat exchanger to reject heat... Right, that heats just gets dumped in the environment. That's important because we're going to use that information very shortly. So again this is just allows us to complete the cycle analysis. Okay, so if we go component by component the analysis looks just like it did for the Rankine cycle, so let's start with our work horse, and that's the turbine. And if we normalize everything by the mass flow rate for the system. And, again, there's only one loop, so there's only one flow rate. And if we assume steady-state, steady flow, neglect the kinetic and potential energy effects, we get this lovely, very simplified system of the enthalpy at state 3 minus the enthalpy at state 4 is going to be the power out of the turbine, just like we had before with the Rankine cycle where it's just the difference in enthalpies across the turbine. We can do the same thing for the compressor, and again, in the Rankine cycle that would be the pump. But it serves the same purpose, so that's going to be the enthalpy at State 1 minus the enthalpy at State 2. Now, if we invoke the ideal gas law, and we assume that we have constant specific heats, so let's write that down. Assume ideal Gas model with constant specific heats. We know that the enthalpy difference is governed by the specific heat at constant pressure times the temperature difference between the inlet and the outlet of the turbine. And we can make the same simplification for the compressor. Okay. Now if we go and analyze the burner, which is again a heat exchanger, we know that that's, let's go ahead and call that, we're going to call that the combuster. we know that the There's no work transfer. Again, we have one mass flow rate in the system and we have heat into the system. So we can just label it like that. As the enthalpy deference across a combustor. And again we can invoke that ideal gas model. To reduce this to an expression that is just the temperature difference. Okay so all of that hopefully looks good to you. There's only two work transfers in the cycle. So this is work transfer out. This is the work transfer in. So we know that for our cycle efficiency we have the network for the cycle. divided by the heat transfer in. And so we can take those terms and substitute them in so that's going to be the turbine work plus the compressor work divided by the combustor heat transfer. You can go ahead and substitute in the enthylpenes and substitute in the temperatures. And you'll see if you go and check any sort of thermodynamics text that we can simplify this expression to ultimately be only a function of the temperatures in the system. And then we could go through exercises on how to improve the cycle efficiency of the air standard Brayton cycle. And we would use the same types of approaches that we used with the Rankine cycle. With is we would put in multiple stages of turbine reheat, we would use multiple stages of inter-cooling, and that's going to all improve the cycle efficiency, but I don't want to focus on that here. What I want to focus on is what you would think is intuitive which is if you were to stand behind a jet engine, which I do not recommend and do not do this, do not do this at home. But you would notice that the heat trans, the temperature of the gases coming out of the back of the jet engine are extremely hot. So this temperature here at T4 is much much greater than the ambient temperature. Let's call that 298 Kelvin. Right? What that means is we are rejecting heat like we do with all power cycles to the environment. And that actually is pretty useful heat that is pretty high temperatures. And so, we look at this system, we think very intuitively hey this is a system that is very right for wastage recovery in other words We can extract more energy out of this system by using the high temperature of the exhaust gases. And that's what we're going to cover shortly. Reheat and inner cooling can improve the cycle efficiency. And just like we did with the Rankine cycle, we can improve the cycle efficiency by increasing the burner operating pressure. Now one key difference between the Rankine cycle and the Brayton cycle is that the compressor work is a much higher fraction of the turbine work compared to the pump work in a Rankine cycle and this is defined as the back work ratio. But recall when we did our example at a Rankine cycle. That the pump was a tiny fraction of the overall work in the system. Where as in this air standard cycle, we do pay a higher penalty because we don't have that phase change. So that's just one of the reasons why phase change is very desirable for power generation because we can move energy around. Much more efficiently than when we don't have a phase change with this Brayton cycle. Now, again, we have a lot of useful energy going out the stack with this basic Brayton cycle. So we're going to see how we can harness that energy. Before we do that, I want you to think about this example question before we start the next segment. This graph shows you a typical, let's say, home or a business or a manufacturing facility. And on the two axes what we see are the electrical energy needs and the heat energy needs. And I've divided that into four quadrants, A, B, C, D. And let's say we have a small business, it's in manufacturing, so they have both a need for, significant need for electrical energy and heat energy. And their target needs are shown as these dashed lines. So what I want you to do is think about what quadrant should they design a combined heat and power system for? So should they design for quadrant A, B, C, or D? Recognize if you're in quadrat A, you're genereating mroe heat than the target, right? Here's my heat eenrgy target. Here's my electrical energy target, okay? So A generates more heat but not enough electrical. B generates both excess heat and excess electrical, etc etc. So go through this thought process and I want you to think about what would due the best quadrant for the operating conditions of a combined heat power system based on this kind of general layout. And that's what we'll start next time. [BLANK_AUDIO]
