COURSE DESCRIPTION This course provides an introduction to the most powerful engineering principles you will ever learn - Thermodynamics: the science of transferring energy from one place or form to another place or form. We will introduce the tools you need to analyze energy systems from solar panels, to engines, to insulated coffee mugs. More specifically, we will cover the topics of mass and energy conservation principles; first law analysis of control mass and control volume systems; properties and behavior of pure substances; and applications to thermodynamic systems operating at steady state conditions. COURSE FORMAT The class consists of lecture videos, which average 8 to 12 minutes in length. The videos include integrated In-Video Quiz questions. There are also quizzes at the end of each section, which include problems to practice your analytical skills that are not part of video lectures. There are no exams. GRADING POLICY Each question is worth 1 point. A correct answer is worth +1 point. An incorrect answer is worth 0 points. There is no partial credit. You can attempt each quiz up to three times every 8 hours, with an unlimited number of total attempts. The number of questions that need to be answered correctly to pass are displayed at the beginning of each quiz. Following the Mastery Learning model, students must pass all 8 practice quizzes with a score of 80% or higher in order to complete the course. ESTIMATED WORKLOAD If you follow the suggested deadlines, lectures and quizzes will each take approximately ~3 hours per week each, for a total of ~6 hours per week. TARGET AUDIENCE Basic undergraduate engineering or science student. FREQUENTLY ASKED QUESTIONS - What are the prerequisites for taking this course? An introductory background (high school or first year college level) in chemistry, physics, and calculus will help you be successful in this class. -What will this class prepare me for in the academic world? Thermodynamics is a prerequisite for many follow-on courses, like heat transfer, internal combustion engines, propulsion, and gas dynamics, to name a few. -What will this class prepare me for in the real world? Energy is one of the top challenges we face as a global society. Energy demands are deeply tied to the other major challenges of clean water, health, food resources, and poverty. Understanding how energy systems work is key to understanding how to meet all these needs around the world. Because energy demands are only increasing, this course also provides the foundation for many rewarding professional careers.
06.05 - More Advanced Methods to Increase the Efficiency of Rankine Power Plants
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From the course by University of Michigan
Introduction to Thermodynamics: Transferring Energy from Here to There
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University of Michigan
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From the lesson
Week 6
In this module, we introduce some of the concepts of the Second Law of Thermodynamics. We will only discuss a small fraction of the vast material that falls under the topic of the Second Law. I encourage you to explore beyond our course material for very interesting discussions on the outcomes of the Second Law which include entropy, the absolute temperature scale and Carnot cycles. The most important aspect for our class, is that the Second Law provides a basis for defining the theoretical maximums and minimums for processes. Using these limits, we can define device and system efficiencies. We demonstrate these limits with examples of basic power plants. A good “take-home” exercise is to apply these limits to some of the devices and systems you see every day around you.
Meet the Instructors
Margaret Wooldridge, Ph.D.Arthur F. Thurnau Professor
Mechanical Engineering, Aerospace Engineering
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.
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