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07.01 - Example of Analysis of a Rankine Power Plant - Part 1: Assigning the State Information (or Pin the Tail on the Donkey)

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Introduction to Thermodynamics: Transferring Energy from Here to There

University of Michigan

4.8 (717 ratings) | 41K Students Enrolled

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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.

Skills You'll Learn

Energy, Energy Systems, Mechanical Engineering, Energy Analysis

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4.8 (717 ratings)

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BS

Jan 18, 2017

I wanted to learn cycle part in Thermodynamics. The professor gave me a new insight in terms of renewable energy, consumption of energy, etc.\n\nThanks. I appreciate your class.

JL

Jul 06, 2017

The course was a great refresher for my upcoming FE exam. I have been out of school for almost 10 years so I really needed this course. Overall the teacher was easy to under

Aus der Unterrichtseinheit

Week 7

In this module we focus on in-depth analysis of a Rankine power plant. The Rankine power plant is the fundamental design for stationary power generation when the working fluid is water (or steam) and the energy carrier is nuclear, coal, gas, or thermal solar power. We also learn that conventional power plants generate a lot of waste heat! Co-generation is a great way to use that waste heat. Can you think of a few ways you might capture waste heat and use it productively? Then you might have your next environmentally sustainable business venture!

07.01 - Example of Analysis of a Rankine Power Plant - Part 1: Assigning the State Information (or Pin the Tail on the Donkey)12:45

07.02 - Example of Analysis of a Rankine Power Plant - Part 2: Finding ALL the State Information11:46

07.03 - Example of Analysis of a Rankine Power Plant - Part 3: Putting it all Together, Cycle Analysis13:59

07.04 - Example of Analysis of a Rankine Power Plant - Part 4: What the Results Tell Us10:34

07.05 - How we can Dramatically Improve Thermal Efficiencies - An Introduction to Waste Heat Recovery8:54

07.06 - Let's Look Inside a Jet Engine3:56

Unterrichtet von

Margaret Wooldridge, Ph.D.
Arthur F. Thurnau Professor

Welcome back. So, why do we use water as the working

fluid for Rankine Power Plant? Well, because right now, and I've

mentioned this a couple of times along, already, so hopefully, you already got

this. That water is abundant, safe, and free.

And the free is for now, because as we'll see in the example we're going to cover

in the next couple of segments, we're going to use quite a bit of water for

these Rankine Power Plants. And we typically prefer fresh water.

So, for all those countries that are land locked, there's a lot of competition

between fresh water that's used for agricultural purposes, for society and

for power plants. Salt water, while abundant, is typically,

obviously, located on the shores. But in addition to that, salt water is

very difficult to work with in terms of its durability on the components that we

use. We don't want salt to be coming, to

precipitate in our components and cause problems with the hardware and with the

length of time between having to take the power plant offline and things like that.

So, fresh water is preferred. It's abundant, it's safe and it's free.

The next type of power plants we're going to cover are going to use air.

Which is also abundant, safe and free. But it's going to take us a little while

before we get to those examples. So for now, let's consider our steam

powered plants. Okay, this is going to take us a while to

get through but we're going to, we're going to use all of our tools.

We're going to consider a steam power plant that uses one stage of reheat.

We're going to have a steam generator, remember that means it's a boiler plus a

steam heater. And it's going to operate at 100 bar.

The condenser will operate at 1 bar. The reheater is going to have an inlet

pressure of 25 bar. If we assume there are no losses in the

system, so we're going to treat this as an ideal system.

we're going to consider the inlet temperature of the first stage of the

turbine is 600 degrees Celsius. And the inlet of the second stage is also

600 degrees Celsius. That's the second stage of the turbine.

So, for this analysis, ultimately, what we want to determine is what is the cycle

efficiency of the power plant. But it's going to take us a lot of work

before we can get to that calculation. So we're going to do this step by step.

Our first step is to make sure that we understand what the system looks like

just on a sketch on a temperature entropy diagram.

To do that, at the same time, we're going to draw our schematic that shows all the

components and label the states. So we can map the states to the T-s

diagram and vice versa. Okay, for each time we ask for state

information, I want you to pause as you play back this video.

And I want you to see if you can answer each question before you continue.

This is a great test of your thermodynamic skills that we're trying to

develop. Okay, so there's our given statement.

Let's get started. So we wanted to sketch the cycle on a

temperature entropy diagram and draw the schematic at the same time.

So, let's get that done. Here is temperature entropy.

Now remember, this is a Rankine cycle, so we're going to have the vapor dome, or

the saturation region. And this is going to be contrary to our

air power cycle, which we're going to see later.

Okay, so again, we're going to draw our basic components of our rankine power

cycle. We have our pump, we're told we have a

steam generator. And we're not going to break this into

two heat exchangers, we're just going to model it as one continuous heat

exchanger. So here's my steam generator.

We're going to enter the turbine, and we're told specifically that we have two

stages of turbine. So, the first stage, we're given

information. And then, the steam goes into a reheater,

which is modeled as a heat exchanger. And again I'm going to show these in

series even though that the turbine stages will be on the same shaft, the

heat exchangers will share a common features as well.

But if this allows it, it'll be little easier for us to analyze.

So here is the second stage of the turbine, so I'm going to call this T1, so

this is the first stage of the turbine. There's the second stage, T2 and here's

my reheater, and we leave the second stage of the turbine.

We go through our condenser, and then that completes our cycle.

Okay, we always like to start with the entrance of the first stage of the turban

as state 1. So there's state 1, state 2, state 3,

state 4, state 5, and state 6. Okay.

So here's my temperature entropy diagram, I have my saturation region.

Remember, my hint to you for how to draw this cycle on the temperature entropy

diagram is to first determine how many isobars, or how many constant pressure

lines you need. And because we're considering this system

as being no losses or ideal, that means every heat exchanger is isobaric.

So we go and look closely at our heat exchangers and the number of heat

exchangers and that's going to tell us how many isobars we have.

But we need to be a little bit more thoughtful than just count the heat

exchangers. But let's start there.

We have the steam generator, so that's one heat exchanger, and one isobar.

And because this is the high-energy condition that goes into the turbine,

this is the high-pressure line in our system.

Then, we have the reheater, which is another, again, heat exchanger here.

And we look and see, well clearly there has to be a pressure decrease across the

turbine, because we're extracting energy from the turbine.

So we know that there's a pressure at state 2, here, P2.

And then at P3, we know that these two pressures are equal.

Right? So, from two to three, because we're,

again, no losses in the system, this is an isobar and this process occurs along

the isobar. This heat edition at constant pressure.

And then we decrease in pressure as we extract more energy out of the second

stage of the turbine. And that takes us to the inlet of the

condenser and again the condenser is heat exchanger, so it is an isobaric process

when there are no losses. So we look at the system and see there

are three isobars high, medium and low. So we come over to our temperature

entropy diagram, and we draw those isobars.

So high, medium, and low. Okay.

Now. Let's go ahead and label the energy

transfers on our system schematic. Again, we have heat transfer in.

We have heat transfer one, this is a first heat edition that we have in the

cycles. So that occurs at the steam generator.

We generate work out, and this is at the first stage of the turbine.

And then we add heat again at the reheater, so there's Q in and I'll label

that 2, because that's the second time we add heat.

And then at the second stage of the turbine we extract work out of the

turbine again. At the condenser, we have heat out.

And then at the pump, we have to add work in order to increase the energy of the

fluid to the high pressure condition. So this is the work in at the pump.

Okay, so just reiterate, we have two heat transfers in.

We have two work transfers out. And that's because we have a single stage

of reheat. Okay, so, we've got all this information

with the energy transfers, we'll come back to our diagram for the temperature

entropy. And let's start with, again, the high

energy state as state 1 at the entrance of the turbine.

And again, if the turbine is ideal. Remember, we call that an isotropic

expansion process, as we expand and draw work out of the turbine, from state 1 to

state 2. Okay, from state 2 to state 3, we have

constant pressure heat addition because this is a heat exchanger.

And we're told the reheater has an inlet pressure of 25 bar and that the inlet

temperature, the first stage of the turbine is 600 degrees C.

So, we could go over here and we could label this 600 degrees C, and we're told

that the inlet of the second stage is also 600 degrees C.

So, we're going to look at this isobar. We're going to follow the isobar up until

the temperature reaches 600 degrees C, and max the exit condition for the

reheater. Okay?

So we want these to all be on the same line.

Okay? From there to four.

Again, we're going expand though the turbine.

And this may or may not be to the same temperature here.

We don't know that. Okay.

So, maybe I should emphasize that this at a slightly different condition than the

other exit stage in the turbine. And then, we're going to condense and

draw heat out of the system until we reach a fully saturated liquid.

So remember, we always like to define the exit condition of the condenser as being

fully saturated or having a quality of zero.

So that's going to define this condition here of state five.

Now, from five to six we need to go from the pressure of the condenser to the

pressure of the steam generator. So be careful, we know again the pump

should be, if it's ideal, and there are no losses, Isotropic.

So this is a constant or a straight line vertical line.

And we have to remember to go past the middle isobar and go to the highest

pressure in the system. Because this is how we connect back to

the steam generator. And that's going to be state 6.

And that maps all of these states onto this diagram correctly.

And if we wanted to be even more specific, we could label each of our

isobars here. That will also help us when we go to

analyze the system quantitatively. So P medium if you will.

So medium, low and high. P high is 100 bar.

P medium is 25 bar. Again, we have 600 degrees C as defined

as the entrance condition or the turbine at both stages.

Then, let entrance temperature. And then we have one bar for the lowest

pressure in the system, and then we condense to the fully saturated liquids.

So again, that gives us the anchor. And we've used all the information that

we know about these devices, the isotropic behavior of the pumps and the

turbines, and the isobaric behavior of the heat exchangers.

Super. Okay, so now we have these sketches, and

for any time you do any analysis, you want to have a state diagram.

And you want to have the sketch. Because that's going to be really

important in reinforcing what we know about the system.

So as we go to the next step, is to go through and identify the state conditions

for every state on that diagram. That's what we're going to do in this

analysis. It's going to take us a while.

And that's one of the hardest parts about thermodynamic analysis of power plants.

So that there's a lot of information, and there's a lot of work for us to identify

the state conditions. So, it's going to take us some time, and

we're going to have to use all of the process information for all of those

states. So the first step is actually the

easiest, which is to identify the enthalpy using the online steam tables,

for the states that we can. Now remember, our online steam table

percolator, we have the limited access edition of it.

So we can only identify states for a limited region of pressures and

temperatures and things like that. So we're going to use it for just a

couple of the states in today's, or in the next few units of discussion.

But I'm going to give you some excerpts of data table that we're going to use to.

And that's a really good exercise for us to understand how to use look-up tables

for, for the steam information. So, what I want you to do first, is to go

online, so pause your video for a moment and go to the online calculator and

determine the enthalpy very specifically at state one.

We're going to go through step-by-step, so let's just start with state one.

And find that information and when we come back we'll check and see if you got

the right answer. Thank you.

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