Concepts of Thermodynamics
Prof. Suman Chakraborty Department of Mechanical Engineering
Indian Institute of Technology, Kharagpur Lecture – 63
Carnot Cycle and Rankine cycle We have discussed about various thermodynamics
cycles so far and we will continue with that. The thermodynamic cycles that we have discussed
so far are mainly air standard cycles, that means, the cycles which use air as working
fluid under certain special assumptions. But practical cycles may not always have air
as a working fluid, but they can use, for example, liquid vapour mixture or superheated
vapour for achieving a particular purpose. And those kinds of cycles may be used for
various applications or those kinds of cycles may find their applications in various sectors
ranging from power plant engineering to refrigeration. So, we will start with something which we
call as vapour power cycles. The whole idea of dealing with vapour power
cycles is to understand the thermodynamic aspects of power generation in a thermal power
plant. And let us try to understand through the following
analysis of cycles. First, we consider an idealized cycle which
we have discussed earlier, and for any thermodynamics cycle that is like a benchmark with respect to which we compare the performances
of other cycles and this is the good old Carnot cycle. So, imagine that there is a boiler. So, remember that every cycle may not always
have an engineering architecture to represent its functionality. At the same time, if we refer to an engineering
architecture or an engineering block diagram which connects various components of an engineering
system to constitute the various parts of the practical cycle, it gives us a good practical
perspective of where the cycle can be applied. So, for understanding the Carnot cycle, bringing
the boiler or turbine or condenser or compressor to a purview is not always necessary. You can have an abstract Carnot cycle where
you have two reversible adiabatic and two reversible isothermal processes, but if you
bring that in perspective with respect to certain physical devices - connectivities
of physical devices, it explains the context much better. So, you have a boiler. From the boiler, so in the boiler what happens? You transfer heat, so that water gets converted
into steam or water vapour. Then it enters a turbine and it expands in
the turbine. Once it expands in the turbine, the thermal
energy of the fluid decreases; and at the expense of this decreased thermal energy,
the turbine gets some mechanical energy, and the turbine blade start rotating. So, that is how thermal energy is converted
into mechanical form of energy and subsequently, to electrical form. Then we have a condenser. The purpose of the condenser is that the steam
condenses from a mixture of saturated liquid vapour - mixture of liquid and vapour to a
state where it is more it is closer towards the saturated liquid. In other words, the liquids the mixture of
liquid and vapour gives away heat to a fluid and then it starts condensing. So, it gives away heat typically to a fluid
which is the cooling water. And I will discuss later on what are the practical
perspectives to it. Then here the pressure is much lower than
the boiler. So, to bring it back to the state of the boiler,
you require a compressor. So, let us try to imagine that there is a
Carnot cycle like this, and plot it in the temperature versus entropy diagram. So, a Carnot cycle in a Ts diagram looks like
a rectangular box. And let us draw that rectangular box, we have
discussed this earlier. So, how does it look like a rectangular box
that, I am not going to discuss over again, but briefly, you have the steam entering the
boiler, sorry water entering the boiler and getting converted into steam. So, from 2 to 3 is the process in the boiler,
then this is a reversible isothermal process because the fluid here is a simple compressible
pure substance. So, its phase change occurs at a constant
temperature. Therefore, a isothermal process is clearly
achievable between stage 2 and 3, this is not at all impractical. From 3 to 4, you are having a reversible adiabatic
expansion in the turbine. So, this is 4. From 4 to 1, you have the condensation process. So, now, if you present the cycle to somebody,
the first question that will come is that so many people say that the Carnot cycle in
a practical consideration is not feasible, but here you are showing that there is a Carnot
cycle based on a power plant may work. So, where is the fallacy? We have discussed about this Carnot cycle,
but we have not discussed the practical feasibility of this cycle, and let us discuss about that. So, practical feasibility-wise 1 to 2, sorry
2 to 3 is ok, 3 to 4 - what is the problem with 3 to 4? First of all, achieving a reversible adiabatic
process is difficult. But even if you achieve that you see that
as the steam is expanding, the state 4 is coming more and more away from the saturated
vapour line. That means, if you expand it more and more,
you will see it goes closer, it goes closer and closer to the saturated liquid line in
the liquid vapour dome, that means, the liquid fraction in the steam that comes out of the
turbine maybe quite high. What it can do? It can erode the blades of the turbine and
that can be pretty detrimental for the performance of the turbine. So, turbine blade erosion is a very, very
practical problem. And because of such problems, you cannot really
go on expanding the state from, say 3, to further and further down. Had you been able to go to lower and lower
temperature, it would actually been better so far as efficiency is concerned, because
efficiency of the Carnot cycle is 1 minus TL by TH; and this is TL and this is TH. So, point 4, had it got lowered; that means,
TL would have been lowered and had TL been lowered efficiency would have been higher,
but practical considerations do not permit that. However, the most impractical part of this
Carnot cycle based thermal power plant is that suddenly stopping the condensation at
the point 1 to achieve a Carnot cycle. So, in a practical plant, how would you know
that where is this point 1? So, it is very, very difficult, I mean you
cannot have a physical mechanism by which you suddenly stop the condensation at 1, so
that is another practical point. The other important practical limit is the 1 to 2, this compression it handles what? It handles a mixture of liquid and vapour. And it is quite a power consuming process
to compress a mixture of liquid and vapour. First of all the compressibility of the liquid
and vapour they are different, so compressing their mixture as a whole is difficult and
because there is significant amount of vapour in the mixture, remember that for a reversible
process steady flow process the work done is v dp. So, the compressor work is v dp because there
is significant vapour in this, this is not completely liquid. So, vapour has a high specific volume and
therefore, the work input to compress the vapour component at least is quite high. So, why do you bother so much about the work
input? You bother so much about the work input because
the net work is the difference between the turbine work output and compressor work input. So, if you require large compressor work input,
then the net work output decreases. And how much it decreases? It is given by a particular parameter called
as work ratio defined as the net work by the turbine work. So, in practice, you want the compressing
device demanding as less amount of energy input as possible. In other words, you actually want the work
ratio to be as close to 1 as possible. It will definitely be less than 1, but closer
to 1, the better it is. So, here because of mixing of because of compressing
this liquid vapour mixture, there are practical difficulties as well as there is a reduction
in the work ratio. So, we have identified various shortcomings
associated with the Carnot cycle, but despite the shortcoming the Carnot cycle give certain
basic understanding that if you decrease TL and if you increase TH, you could increase
the efficiency of the cycle. So, in reality if you do not have a constant
TL and constant TH, that is constant temperature of heat rejection and constant temperature
of heat addition, you could work out an average temperature of heat addition and average temperature
of heat rejection, and replace this instead of the TL and TH; you write average TL and
average TH. I will define that so called mean temperature
of heat addition and rejection later on. And we can clearly see that lower the mean
temperature of heat rejection or higher the mean temperature of heat addition more will
be the efficiency. So, now given that the Carnot cycle is not
very much practically feasible, we will study a variant of this called as Rankine cycle. So, I will try to draw the Rankine cycle in
the T-s diagram first, and then we will change the hardware to accommodate for that. So, in the Rankine cycle, what we do is, we
have similar process like the Carnot cycle, but we replace the compressor with a pump,
and the pump generally will handle only the liquid. So, the abrupt stoppage of the condensation
process from 4 to in between somewhere which was there for the Carnot cycle. Now that is replaced by a complete condensation
from 4 to 1. This is the major difference between the Rankine
cycle and the Carnot cycle. So, from 4 to 1, 1 is not in between, 1 is
at the saturated liquid state. And then
from 1 to 2, there is a pump which pumps it to pressure to the boiler pressure. So, what it does is that it achieves something
very interesting, it replaces the compressor with a pump which consumes much less power than the compressor. So, that is the game that the pump handles
only the liquid, it does not handle the liquid plus vapour mixture. So, operation wise also pump is much more
convenient than a compressor; power input wise also a pump requires much less power
input because in integral v dp the such the specific volume which comes into the picture
that is much less for a liquid as compared to a vapour, but in reality you know life
is always like a balance. So, when you gain something, you also lose
something. And what is that we lose here? Instead of heat addition at a constant temperature,
now the heat addition starts from state 1 to state 2, sorry state 2 to state 3. So, earlier the state 2 was here, now the
state 2 is here. So, from 2 to 3, it is not the entire heat
addition at the TH - previous TH, some heat addition from 2 to 2’ is at a temperature
lower than TH. So, the average temperature of heat addition
which is defined as this mean temperature of heat addition. So, it is defined as the area under the Ts
diagram from during the heat addition process. So, integral T ds from 2 to 3 divided by the
change in entropy. So, as if had it been a constant temperature
process, what would be the equivalent constant temperature; and here that mean temperature
of heat addition will be something between the temperature at 2 and temperature at 3. So, this is the mean temperature of heat addition. So, because the mean temperature of heat addition
is less than what would have been there had it been a Carnot cycle clearly the efficiency
will be less. But efficiency is not everything in life,
you also have to see other practical constraints. And regarding replacing the compressor with
the pump, the practical advantage of getting a high work ratio is very much there. The reason is that the pump consumes very
little work, so that the net work by turbine work is very close to 1. You can make it closer and closer to 1 by
making other or by taking other measures but efficiency wise we have to sacrifice. So, this sacrifice in efficiency can be compensated
by other arrangements. And we will make those arrangements subsequently. So, this is an ideal Rankine cycle so called
ideal Rankine cycle, but you can have a Rankine cycle where the heating in the boiler does
not stop at state 3 and the heating continuous in the superheated region at the constant
pressure which is the boiler pressure. So that is called as Rankine cycle with superheat. . So, I will draw the Rankine cycle with super
heat in the same Ts diagram to explain you that what happens with the super heat. So, with superheat you will continue with
heating in the boiler up to point 3. And then if you make a reversible adiabatic
expansion, instead of the point 4 here, you will have the point 4 towards the right. So, what are the advantages with this? Clear advantage is that the mean temperature
of heat addition again had gone up which had gone down because of this part. By the way, in the real power plant architecture,
the points 2 to 2’, this takes place in a zone called as economizer, 2’ to this
one, say 2’’, this takes place in the so called boiler, and 2’’ to 3 this is
called as super heater. So, what we loosely called as the boiler part
has essentially three sub parts, economizer, boiler and super heater. Now, this point 4 being earlier it was much
more away from the saturated vapour line, now it is closer to saturated vapour line. Earlier it was here, now it is here. So, when it comes closer to the saturated
vapour line, then what happens? Then the turbine blade erosion problem is
also reduced and that is a big thing because if you reduce the turbine blade erosion problem,
then the blade life is increased, and manufacturing turbine blade this one of the costliest things
for setting up a thermal power plant, so that would make a lot of relief. Not only that the enthalpy drop between the
previous start point and endpoint of the turbine and the present enthalpy drop - the enthalpy
drop now with superheat is much higher that means you get much more specific
enthalpy drop across the turbine. If you get much more specific enthalpy drop
that means you require less amount of steam consume to get the same amount of power, because
the mass flow rate into the enthalpy drop is the power output of the turbine (W dot
turbine). So, if you have greater delta h, delta h is
here h 3 minus h 4, then you have less m dot, so m dot, so m dot is
W dot turbine by delta h. So, this is called as steam consumption at
the rate of steam that needs to flow across the device. So, more this is what is it is because you
have to burn more coal or any fuel to get a particular amount of power. If you get sorry you have to run more fluid
in the not the coal I have mistakenly said that, you have to basically run more fluid
more working fluid in the system, because m dot is the working fluid which is running
across the system. So, you have to run more working fluid to
get the same amount of power. Ok? So, this is steam consumption not fuel consumption,
by mistake I have told fuel. Ok. Now, the question is that superheat gives
all good effects, right? It increases - so three positive effects - one
is increasing the efficiency; the second is reducing the turbine blade erosion problem,
and third is reducing the steam consumption. Ok? So, I mentioned about the fuel, and the fuel
is indirectly related to the steam consumption, because more is the steam consumption more
amount of fuel you need to burn, because for converting from liquid to vapour, the amount
of steam - the amount of fuel is required is proportional to the mass of liquid that
is being converted to vapour, so that is what I am coming. So, I have mentioned about three points which
are very positive. The question is had it been so you should
have increased the temperature to temperature of the state point 3 higher and higher because
had your point 3 been here you would have got more efficiency. Had your point 3 been here, you could have
got even more efficiency. And not only that the turbine blade erosion
problem will also be much less everything will be positive, but we do not do that. The constraint is not thermodynamics, but
material that turbine blade has to be good enough in terms of withstanding the very high
temperature at that state. So, the maximum limit of temperature is restricted
not by thermodynamics constraints, but by material constraints. By material constraints, if you go to higher
and higher temperature, although you will get greater and greater efficiency, but the
material of the turbine blade may fail, so that brings us
to a perspective, where you are not able to go to a very high temperature which you wanted. Had you been able to do that, it would have
been a delight. If you cannot do that, so this is Rankine
cycle with superheat, you simply super heating, may not work. And then to derive all these advantages you
consider, so we considered Rankine cycle, ideal Rankine cycle with superheat, and we
will add another factor which we call as Rankine cycle with superheat and reheat. So, what is reheating? So, what we will do is we extract
the steam not at this state, but at a somewhat intermediate pressure state, say this state
which is state 4. Then we heat it in the reheater. This is physically a reheater. So, this is called as reheat. But you know it could be integrated with the
boiler itself. So, you can, in principle - just to make a
discernible architecture, let me draw a phase diagram, so that it is easier. So, you can have a boiler, a turbine - there
is a extract from the turbine - it goes to a device which is called as a reheater which
may be physically integrated with the boiler, but you may just for clarity show a reheater
like that. And then that reheated steam enters the turbine,
and then from the turbine, the exit state comes. So, you have, so we start with the Ts diagram,
by drawing the Ts diagram, I will not draw on the same diagram again and draw phase diagram. So, boiler 2 to 3; boiler to turbine - expansion,
the first level of expansion from 3 to 4; then at that intermediate pressure, heat is
again added in the reheater. Here we are showing it as a separate block
just for clarity. And the reheater itself may take it to a super
heated state. But, to what temperature? Maximum? So, if we considered superheat plus reheat,
then your point 3 could be beyond the saturated liquid saturated vapour state. So some here may be, so, this is point 3,
this is point 4. So, what I mean is that now from here when
it goes up maximum temperature could be this, because you stop heating beyond this for the
material constant. When you reheat, you cannot heat it beyond
this. So, you go from here to a point 5, where it
enters the turbine. And then from 5 it expands in a turbine - 5
to 6. And from 6 to 1, in the condenser, so this
becomes your point 2 and you have the process like this. So, this is the Rankine cycle with reheat
and superheat. You could have multiple stages of reheat. But here in this diagram we are showing only
one stage of reheat. Remember that had the turbine blade hypothetically
not have any material constraint, reheat is not necessary. Alone superheat would have done the purpose
because of separate attachment. And extracting the steam from the turbine
in between and heating it again all these are problematic. So, we are taking that problem because we
have no way of heating this further in a single shot. So, we are heating it in a sequence of shots. In this way, one significant gain that we
are getting is that we are going more and more closer to the saturated vapour line that
means - so this is the point 6. That means, the point 6 is having much closer
existence to the saturated vapour line, and the turbine blade erosion problem is less. What about the efficiency with reheat? See your average temperature of heat addition
is the average temperature of heat addition during the super heat part plus the average
temperature of heat addition during the reheat part. So, these two effects together can actually
have a higher mean temperature of heat addition as compared to without reheat or could even
have a lower mean temperature of heat addition as compared to that without reheat. So, if you, so this is - this pressure is
called as reheat pressure, and this pressure is may called as the boiler pressure. So, if you make a plot of the change in efficiency
with respect to the original efficiency as a function of the reheat pressure by boiler
pressure, you get a curve like this. This is around 0.25 from practical thermal
power plant data. So, you actually have a deduction in efficiency
if the reheat pressure is very low because if the reheat pressure is very low then the
mean temperature of heat addition because of low reheat pressure you also have a lower
temperature at which heat is added. That will reduce the overall mean temperature of heat
addition. And the efficiency instead of gain has a fall. Beyond that, the efficiency starts increasing
but you get the maximum benefit when this is around 0.25. What is this? So, zero benefit when the reheat pressure
is same as the boiler pressure, That means, it is no reheat. So, this value is 1. Ok? So, to summarize we have discussed about Rankine
cycle, simple Rankine cycle, Rankine cycle with reheat with superheat and with reheat. What we have not discussed is what is the
role of the condenser in the Rankine cycle, and we will take up in the next lecture. Thank you very much.
