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.
03.06 - Steam Turbine Example - Part 1
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来自 University of Michigan 的课程
热力学导论: 能量转移
577 个评分
从本节课中
Week 3
In this module, we introduce our first abstract concepts of thermodynamics properties – including the specific heats, internal energy, and enthalpy. It will take some time for you to become familiar with what these properties represent and how we use these properties. For example, internal energy and enthalpy are related to temperature and pressure, but they are two distinct thermodynamic properties. One of the hardest concepts of thermodynamics is relating the independent thermodynamic properties to each other. We have to become experts at these state relations in order to be successful in our analysis of energy systems. There are several common approximations, including the ideal gas model, which we will use in this class. The key to determining thermodynamic properties is practice, practice, practice! Do as many examples as you can.
与讲师见面
Margaret Wooldridge, Ph.D.Arthur F. Thurnau Professor
Mechanical Engineering, Aerospace Engineering
Okay, so the question we left with last time is do you have enough information to
determine the mass flow rate of steam through the turbine?
So there's a lot of. The short answer is yes of course you do.
The longer answer is of course you need to draw your system schematic and show
okay. Well, you have one entrance and one exit
that's been described. Okay?
So we have some mass flow rate that's coming in.
And some mass flow rate that's coming out.
And remember we, we would look at our conservation of mass.
And we would say, [INAUDIBLE], in the most general form, we would have this
expression. [SOUND] And you say, oh, look.
I know that this is equal to 0, because I've been told that we have a steady
state system. I have one inlet and one outlet, so I
have m in equals m out, which equals the mass flow rate for the system.
And last time we showed you how, in the last segment, the mass flow rate is
completely defined in terms of the density of the fluid at the inlet or exit
state. The velocity at the inlet or exit state,
and the area at the inlet or exit state. So, as long as you have all of this
information, either at the inlet or at the outlet, we can define the mass flow
rate for the system. So, we look up at the given information,
we say okay do I have enough. I'm given the velocity at the entrance.
So, I would write down that I have V1, I have P1 and I have T1 on my diagram.
And at the exit, we're told that the steam leaves the turbine at a pressure
that's known, so I know P2. I also know the diameter at the inlet and
the diameter at the exit, so there's D 2, and there's D 1.
And if we assume that the diameters are, that we're dealing with circular
orifices, circular inlets and outlets. We know that this is going to tell me the
area at the entrance, and similarly this information tells me the area at the
exit. So, I go through my little checklist, and
I say okay, well, at the inlet, I appear to have the area.
At the outlet, I appear to have the area. The inlet, I have the velocity.
Sorry, that's a velocity here. and I have pressure and temperature at
the inlet. I have pressure and I'm told the system
leaves as a dry saturated vapor. You need to convert that into some value,
into some parameter. Thermodynamic parameter and we know that,
that tells us the quality at the exit state is 0.
At the entrance state here, we look and we say that's a pretty high pressure,
that's a high temperature condition. I'm going to guess, and it's a really
good guess, that we're in the super heat region.
In which case pressure and temperature are independent and all the state
parameters are known. At the exit state I have the quality and
the pressure so I know that state is fully defined, those are always unique
parameters. So that tells me I have the density, I
can get the density from state diagrams. Or from online calculators or from tables
at both the entrance and the exit. Now, this is a guess at the entrance that
it's a super heat, and that's going to be valid.
But, again, that's a good guess. And we'll develop that intuition as we
work with these, turbo machinery. And we work with these, these energy
transfer devices. So, sure.
The short answer is, yes. I can evaluate the flow rate using all
the information from the, in, at the inlet condition.
I don't have the velocity at the outlet condition, and that in fact is going to
be the question I'm going to ask you next.
So let's take this information. Let's go ahead and do that calculation.
So again, I have velocity, I have area because I have diameter, I need the
density or specific volume. So remember, we can always write this as
the inverse of the specific volume all at state one.
In the tables they typically will list the specific volume instead of the
density. So just be again very fluent and capable
of moving from one space to the other. So having said that this is a good time
for us to introduce the online calculator that we are going to use for this class.
Again, I'll provide you with little excerpts of tables.
So, we're going to have to use those too. But let's start with just using the
easier tool which is the online calculator.
Okay, so now you can get to the online calculator through this web address
that's shown here, www.steamtablesonline.com.
Now, we don't have full access to all the tables, because we're using the free
version, but that's going to be plenty for our needs.
So we're going to click on Run Calculator for the properties of water and steam.
So, what you want to familiarize yourself with is how to use this program.
It's a really great and fun tool. General Properties are the first tab the
saturation properties are the second. We have steam turbine, flash evaporators.
These are getting more complex as we move across the tabs.
They have the actual temperature entropy diagrams.
We are not going to talk about entropy in this class.
It's another thermodynamic parameter. Enthalpy, entropy.
So it keeps going and keeps going. So we're really just going to stick with
these first couple of tabs in this class. So what we want to do is define, we want
the density as the entrance state so we know that we have pressure and
temperature. So I know they used lower cased notation
here but that's our familiar pressure and temperature here.
And we can see that because it tells me pressure in absolute units of bar,
temperature again, they're using degrees Celsius which is very common.
when we calculate anything with temperature you're going to use Calvin.
But when we look up information on these online calculators you're going to use
Celsius. Okay so we know from our problem
statement that we have inlet pressure of 69 bar.
I'm going to make sure I've got that number and we have an inlet temperature
of 538 degrees Celcius. And we're going to hit calculate and it
propagates this table for us, so again if we come back and we just confirm.
Okay, so 69 bar 538 degrees Celsius and you can see we get everything and
anything we want to know about that state.
It's like It old you. You define two independent and intensive
properties and you get every other property you'd ever want.
So we can see there's temper, these are input conditions here.
Density, specific volume asked, specific enthalpy, anthropy, exergy, internal
energy. You name it, it's all here.
Heat capacity, we talked about our constant pressure heat capacity.
Constant volume heat capacity. But we wanted to come back with whichever
one you want. Either the specific volume or the
specific enthalpy here. And we're going to use that in our
calculation. We'll use the specific volume, the 0.05
0.052 meters cubed per kilogram. Okay.
So, we're going to treat that information as known, we have that.
while we're here, because we want to expedite our process, we're going to
collect information about the saturation state too.
So recall that we had, [INAUDIBLE]. we know that we are a saturated vapor.
We're told that in the problem statement. So not often you won't know whether or
not you're in the saturation region. An so what you would do is, you could
determine that you're in the saturation region through the information you have.
So, if you didn't have the quality, and let's say you put in two parameters here
that put you in the dome. The calculator would say you're out of
the range of this, of the, tables. Okay?.
So let's go to the saturation properties, 'cuz we know that's where we are.
again, notice that we've know changed the input configuration here.
Now we have pressure and quality. And again, you can change those.
Those are all, you know? Look at all the different forms you have
here. You can do pressure, specific volume,
temperature, enthalpy. You have a huge array of choices here.
So, we're going to put in the pressure at the exit, which was 10 bar, and we had a
quality of 100%, because it was a saturated vapor.
And we'll do the calculation and what we want to take back with us is the specific
volume at this condition is 0.001 meters cubed per kilogram.
And be sure you check those oh, I'm sorry, we wanted this, it took me to the,
I read the wrong side. That's the saturated liquid result, we
want the saturated vapor result. My bad, my apologies, I read the wrong
column. So we take 0.194 meters cubed per
kilogram. And again, make sure you get the units,
that you're always checking your units, because we can be dangerous when we have
these tools. And we just use them as a black box.
So, we're going to take that number back with us and we're going to go back to do
our calculations for the mass flow rate. Okay, here we are back at our
calculations for the mass flow rate. So, we went to the steam tables, our
online calculator, and we got that density at State One.
So, now we can plug in all the information that we have from the problem
statement. We have 64 meters per second times the
area, which is going to be Pi over 4 times the diameter at the entrance
squared,. So that's 0.45 meters squared divided by
the specific volume at the entrance state, which we looked up from our
calculator and we found it was 0.0518 meters cubed per kilogram.
And, we always include our units. And, we look and we say, "Ooh look,
meters squared times meters gives me meters cubed," so those cancel.
And, if I crunch through on my calculator the math we come up with a number of
196.5 kilograms per second. That's the mass flow rate of, through the
turbine. So couple of things.
You always want to step back, look at your number.
Does it make sense? That's a lot of mass moving through a
steam turbine. And that's pretty realistic.
Okay. That's a pretty good number.
Again, I wouldn't expect you to necessarily have a feel for that unless
you work in turbo machinery. But we'll start developing a feel for
what numbers make sense. A hundred and ninety-six kilograms per
second. We check to make sure our units make
sense, and indeed they do. It's a mass flow rate, so it should be
mass units per time. We make sure our sines are correct, and,
of course, in this system, there's no sine.
You know, we don't, we're not differencing anything, so of course it's
positive. Cool.
So we understand how to do those types of calculations.
So we just did the mass flow rate. That calculation, we went through that
whole process. What does the velocity, the speed, of the
steam at the exit of the turbine? And do we have enough information to
determine that? Well, of course we do.
That's why I set it up for you. So what is the exit velocity.
So what is the 2. Okay.
So we go through the same process that we did before.
Well we know that the mass flow rate is given by this expression at the inlet
outlet. So, if this is what we're looking for,
here, we just solve for we solve for the velocity at the exit, and of course we
did this in terms of specific volume. So I'll switch to specific volume here
And again, A2 is, is already, we know the diameter.
We already went to the steam tables and saturation tables and we got the density
at the exit state. And so, we just have to, again, turn the
crank. And so, we take our previous number of
196.5 kilograms per second. And we, we have area here so we have pi
over four, the diameter at the exit again is larger so that's going to be 3.6
meters squared. We multiply that by the density we found
not he table, which was, found on the online calculator.
Which was .194 meters cubed per kilogram, and we go through and determine that
velocity at the exit is 3.5 meters per second.
And again the kilograms here will cancel, meters squared canceled with cube,
leaving me again these units. So again the system helps me by saying I
checked my units. It confirms that that's correct.
We look at the number and say, "Does that look reasonable?" and, again, I don't
expect you to have a good feel for speeds of [UNKNOWN] at this point in time.
But we'll develop those tools as we go through this class.
The other thing that's really useful as you go through these types of exercises.
Is for us to look at things like, okay well, the mass flow rate we know is
proportional to density. It's also proportional to diameter
squared and to speed. So if we wanted to like double the
diameter we're going to have a quadratic effect on the mass forwarding.
So it's good for us to understand these ratios.
For us to understand what happens as we change physical dimensions or as we
change thermodynamic properties. So those are the types of things that you
should always step back at the end of a problem and don't be satisfied with just
the number. Look at what you've learned in this ex-,
in the whole process. What have you understood in terms of the
general features of the system. Okay.
So, we've gone through and we've determined the mass flow rate through the
steam turbine. We've looked at the velocity, and we've
determined quantitatively the velocity at the exit of the steam turbine.
We did this by looking up the information we needed in the steam tables.
In this case, the steam online calculator.
So that introduced us to that tool at the same time.
Now what I want you to do is sketch for me what this process looks like as the
steam enters the turbine at state 1. An exit the turbine at state 2.
So put that on the PV diagram. I want you to include the dome and label
states at the inlet is 1 and the exit at state 2 and that's where we start the
next unit. Thank you.
