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Hello and welcome to lecture number 21 of
this lecture series on turbo machinery aerodynamics.
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We have been discussing about turbines, and
in particular, axial flow turbines in the
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last few lectures; and we had a chance to
discuss about quite a few things about axial
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flow turbines, we started off with the very
basics of turbines in general, which is basically
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to do with the thermodynamics turbines; and
after having a very detailed discussion on
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the thermodynamics of flow through turbines,
we have also discussed about the types of
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turbines; and we have seen that there are
basically three types of turbines possible:
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one is axial flow turbine, the radial flow
and the mixed flow turbines.
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And we have been talking about the axial flow
turbines in the last couple of lectures; and
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in the last class, we have discussed about
the fact that there are basically two configurations
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of axial turbines, which are possible: one
is the impulse turbine and the other is the
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reaction turbine; and when I discussed about
these two different types of turbines, I happened
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to mention that the reason why they are, this
this distinct classes of turbines is the fact,
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that the way stagnation or enthalpy drop takes
place in a turbine is different in these two
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different types of turbines.
Now, in a turbine stage, we know that turbine
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stage basically consists of a stator or a
nozzle, followed by a rotor. There is certain
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amount of pressure drop taking place in the
nozzle, and there could be certain amount
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of pressure drop taking place in the rotor
as well, but there are certain types of turbines
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where the entire pressure drop or the enthalpy
drop takes place only in the nozzle, and the
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flow simply undergoes a turn as it passes
through the rotor. So, these types of turbines
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are called impulse turbines; and there are
also types of turbines where the pressure
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drop or enthalpy drop is split or shared by
both the nozzle as well as the rotor; and
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these are known as reaction turbines. So,
these are the two different or distinct types
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of turbines, which we had talked about.
In today's class, when we began with, we will
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basically be talking about a parameter, which
can be used as a parameter to distinguish
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between these two types of turbines. So, that
is one of the main things that we are going
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to discuss about; we will start the lecture
with discussion on what is known as degree
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of reaction; after that, we will be talking
about the losses encountered in turbine, what
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are the different forms of losses and subsequently,
we will also be talking about the efficiency
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or different forms of efficiency in a turbine.
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Now, when we talk about losses, there are...
Well, we have already had a very detailed
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discussion on well 2-D as well as 3-D losses
in the context of axial compressors. It is
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the exact same concept which can be also used
in a turbine, therefore I will not really
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go into the details of different types of
losses and how it can be estimated and so
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on, because we have already talked about that
in the case of compressors, we can simply
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extent that to turbines and so rather not
repeat the same thing here, but I will of
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course, go through the essentials of losses
in a turbine, and also how it can estimated
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in a very generic sense and without going
into too much of details, because they have
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already been covered in compressors; and then
we will talk about efficiency, and what are
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different types of efficiencies, in fact,
in turbines you can have different forms of
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efficiency, there are at least four or more
different types of efficiencies that can be
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defined for a turbine, but we will restrict
our discussions to two forms of efficiencies,
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which are more commonly used; one is known
as the Total-to-static efficiency and other
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is known as the Total-to-total efficiency.
There are also static to static, and there
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are other types of efficiencies which are
not really used commonly, and so we will not
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discuss those in a great detail. So, let us
start our discussion with degree of reaction,
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and what we mean by degree of reaction, and
how it can used in a turbine.
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Now, degree of reaction as you have seen in
the case of compressors, is a concept which
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is used to kind of understand, how much amount
of work sharing is done by the rotor as a
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comparison of the entire work done in a stage,
and so in the case, in the context of a turbine,
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here the flow basically undergoes acceleration
as you already know by now, that it is an
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accelerating flow in a turbine, and acceleration
takes place both in the nozzle as well as
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in the rotor, and therefore as a consequence
of that, there is an enthalpy drop taking
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place both in the rotor, well, in the nozzle
as well as the rotor; degree of reaction gives
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us some idea about well, it it is basically
an indicator of the amount of enthalpy drop
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that is taking place in the rotor or in the
rotor as compare to the enthalpy drop taking
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place across the entire stage; so, that is
the basic significance of degree of reaction.
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So, but before we go into details of degree
of reaction, let us take a look at the typical
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velocity triangle, which I had discussed in
detail in the last class; let me quickly recap
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what this velocity triangle means.
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This is the typical stage of an axial turbine,
which consists of a nozzle and a rotor. So,
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flow enters the nozzle at an absolute angle
velocity of C 1, which is at an angle of alpha
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1, leaves the nozzle at velocity of C 2, which
is the absolute velocity, and making an angle
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of alpha 2 with the axial direction; V 2 is
the relative velocity, which makes an angle
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of beta 2 with the axial direction; and then
flow from this enters into the rotor, and
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leaves the rotor with relative velocity of
V 3, making an angle of beta 3 with the axial
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direction, and C 3 which is the absolute velocity
makes an angle of alpha 3 with the axial direction;
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the blade speed in both at the inlet as well
as the exit of the rotor is assume to be the
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same and equal to U.
So, this is the very typical or a generic
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velocity triangle applicable to any axial
flow turbine, and so our definition of degree
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of reaction is with reference to since its
with reference to a very generic axial turbine,
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it can be used in whether in in the case of
impulse turbines as well as for the reaction
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turbines, and what we will see very soon is
that impulse turbine is a special case of
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zero degree of reaction turbine that is when
the degree of reaction is 0, then that turbine
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refers is is basically an impulse turbine.
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So, as I had mentioned earlier, degree reaction
is defined as static enthalpy drop in the
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rotor divided by stagnation enthalpy drop
in the stage. So, if you look at the rotor,
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these are the station, it is between station
2 and 3. So, static enthalpy drop is h 2 minus
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h 3 divided by h 01 minus h 03 that is for
the stage; well of course, we can always say
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that h 01 is also equal to h 02, because in
the stator, there is no enthalpy change - stagnation
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enthalpy change. Now, so if we if we look
at a coordinate system, which is fixed on
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the rotor or in the relative frame of reference,
the appearance stagnation enthalpy is basically
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a constant;
And so, we have h 2 minus h 3 is equal to
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V 3 square by 2 minus V 2 square by 2. So,
if the axial velocity is assume to be the
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same upstream and downstream of the rotor,
then this can be reduced to h 2 minus h 3,
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which is stagnation static enthalpy drop in
the rotor, is a one-half of V w3 square minus
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V w2 square which is half of V w3 minus V
w2 multiplied by V w3 plus V w2. We also know
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that the stagnation enthalpy change across
a stage, which is give by h 01 minus h 03,
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is basically a function of the blade speed
and the change in the tangential component
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of the absolute velocity that is U times delta
C w is basically in this stagnation enthalpy
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drop. Therefore, h 01 minus h 03 is also equal
to U times C w2 minus C w3.
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So, let us simplify the degree of reaction
here. So, degree of reaction would become
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V w 3 minus V w2 multiplied by V w3 plus V
w2 divided by 2U into C w2 minus C w3. Now
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if you go back to the velocity triangle, let
us go back to the velocity triangle here,
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if you look at the components or the difference
between C w3 and C w2 that is basically equal
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to the difference between V w2 and V w3 that
is in their tangential direction; therefore,
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V w3 minus V w2 is basically C w3 minus C
w2 and so, this degree of reaction will basically
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reduce to minus V w3 plus V w2 divided by
2U. Now from the velocity triangle, you can
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also see that V w3, which is the tangential
component of relative velocity at the exit
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of the rotor is C a times tan beta 3. Similarly,
V w2 is C a tan alpha 2 minus U. So, degree
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of reaction basically reduces to half of 1
minus C a by U tan alpha 2 plus tan beta 3.
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So, this is one form of defining the degree
of reaction that you can relate degree of
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reaction. We have seen this definition even
for compressors and we have also seen that
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degree of reaction is a function of a few
parameters; one of them of course, it is the
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ratio of axial velocity to the blade speed
C a by U, besides that there are the angles
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alpha 2 and beta 3 in this case. So, it is
a functional of the angles as well as the
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the axial velocity and the blade speed.
So, we can also simplify this, in in the sense
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that if you look at zero degree of reaction,
and also look at a 50 percent degree of reaction
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turbine; we will see, what are these special
cases of axial turbines where we can look
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at an impulse turbine, and then 50 percent
degree of reaction turbine. So, degree of
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reaction starting from the fundamentals its
basically ratio of enthalpy drop - static
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enthalpy drop in the rotor divided by stagnation
enthalpy drop in the stage which we can simplify
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as we have seen, and relate degree of reaction
to the flow coefficient which is C a by U,
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and the angles; in this case, it is the absolute
angle, at the inlet of the rotor and the relative
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angle or the blade angle at the exit of the
rotor that is tan alpha 2 plus tan beta 3.
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So, let us look at some special cases of degree
of reaction. Now, if you look at a symmetrical
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velocity at triangle configuration where alpha
2 is equal to minus beta 3, what we will see
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that we get the degree of reaction as 0.5.
So, this is known as a 50 percent degree of
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reaction turbine, we have seen this in the
previous lecture as well; in other special
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cases, when V w3 is equal to minus V w2, then
we get degree of reaction as 0, which is basically
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an impulse turbine. So, if we were to look
at an impulse turbine little more carefully
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and compare that with degree 50 percent stage,
for a give stator outlet angle that is alpha
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2, the impulse turbine stage requires a much
higher axial velocity than the 50 percent
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reaction stage.
In the impulse turbine, it is generally seen
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that all the flow velocities are higher, and
therefore, it is generally also seen that
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the efficiency of an impulse turbine is usually
lower than that of a 50 percent reaction stage,
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for two turbines which are generating the
same power; that is of course, a generic general
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observation that because of velocity components
are higher, the losses are likely to be higher,
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and therefore, efficiency is usually slightly
lower than that of a 50 percent reaction turbine
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stage.
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So, let us look at these two special cases;
this is the impulse turbine stage, we can
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see that the V w3 or V w2 will be equal to
minus V w3; If that is so, then the degree
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of reaction becomes and 0, and such as turbine
is an impulse turbine stage. So, we have V
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w3 and V w2, which are opposing each other
and equal in magnitude that is what we have
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degree of reaction as 0, and what are the
physical implications of this... In in degree
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of reaction 0, it means that there is nothing
much happening in the rotor as far as enthalpy
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drop is concerned the rotor simply deflects
the flow, and there is no change in the enthalpy
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in the rotor, and that is why degree of reaction
is 0, because if there is no change in enthalpy
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in the rotor, the numerator is 0, degree of
reaction is 0.
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Now if you look at a 50 percent reaction turbine
stage, then we have the angle it is a symmetrical
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velocity triangle, and therefore, alpha 2
will be equal to beta 3. So, if those angles
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are equal in magnitude, then you get velocity
triangles which are symmetrically, you can
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see that this is the velocity triangles are
basically mirror images, what you have at
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the inlet is mirrored at the exit. So, that
is why you have symmetrical or mirror image
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velocity triangle; if the reaction turbine
is a 50 percent reaction stage, and what it
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means is that the enthalpy drop is shared
equally between the rotor and the stator,
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and that is what a 50 percent reaction stage
basically means.
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So, what we have defined in the last few minutes
is, this is very important concept of degree
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of reaction, where which basically tells us
the amount of enthalpy drop, which is shared
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between the rotor and the stator; and how
we can, you know use that as a parameter to
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distinguish between these two types of turbines;
impulse turbine where you have degree of reaction
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as 0, which means that there is no enthalpy
drop taking place in the rotor, and we have
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seen that such a velocity triangle, we have
the tangential component of relative velocity
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V w3 is equal to minus V w2; they are equal
in magnitude, but they are opposite in direction,
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and that is why in the velocity triangle,
you can see that they will oppose each other,
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when you take up their components; 50 percent
reaction stage, velocity triangles are symmetrical,
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and you have alpha 2 is equal to minus beta
3. So, well these angles are same making the
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triangles symmetrical or mirror images across
the rotor.
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So, now that we have discussed about degree
of reaction; let us move on to a very important
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aspect of performance of turbines that is
the efficiency. I think, I have mentioned
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in the beginning of the lecture that efficiency,
in the case of turbine unlike in compressors,
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we have in turbines defined in different ways,
basically depending upon the application for
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which the turbine is being used. Now, there
are certain applications, let us say in a
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land based gas turbine power plant where you
you generate, you are using a gas turbine
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to generate power. So, here the application
is such that you do not want the turbine exhaust
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to have any very high levels of kinetic energy,
because that is getting wasted. So, you would
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like to use up as much as kinetic energy as
possible from the turbine itself without having
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to waste kinetic energy.
So, here we would like to expand it to the
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minimum possible enthalpy - static enthalpy,
and therefore, any kinetic energy that is
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there at the exit is considered a waste. So,
in such turbines, we usually define efficiency
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in the form of what is known as Total-to-static
enthalpy, and the other form of enthalpy that
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we are going to define is known as Total-to-total
enthalpy, which is what is of interest to
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aero engineers, because in a gas turbine engine
which is used in aircraft, for example, there
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is enough kinetic energy available at the
turbine exhaust, which can be exact again
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expanded or further expanded through a nozzle
to generate thrust, and you do not want the
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turbine exhaust to get or turbine to exhaust
itself to the minimum possible kinetic energy,
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because you would also like to expand further
in a nozzle generate thrust.
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So, in such applications, you one would prefer
to define efficiency based on Total-to-total
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or stagnation enthalpies. So, these are the
two commonly used forms of efficiencies as
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I mentioned, there are also other forms of
efficiencies, which are not very commonly
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used like static to static and so on. We will
restrict our discussion to this two types
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of efficiencies: Total-to-static and Total-to-total
efficiencies.
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Now, so some general comments which I had
main, let me list down here. So, the aerodynamics
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losses in a turbine as we have seen differ
with the stage configuration are the degree
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of reaction, and so improved efficiency is
associated with the higher amount or level
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of reaction, which implies less work per stage,
and therefore, higher number of stages for
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a given overall pressure ratio. So, the reason
why we need to understand efficiency or the
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sources of losses is that it firstly helps
us in making a choice between different configurations
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either degree impulse or a reaction, but the
other advantage is that it will also tell
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us how one can control these different forms
of losses.
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So, based on our understanding, we can define
two types of efficiencies, Total-to-static
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efficiency and the Total-to-total efficiency;
and which efficiency definition to use will
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basically be determined by the application
for which the turbine is being used. So, in
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let us say the land based power plant as I
mentioned, the turbine output is a basically
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in the form of shaft power that is the turbine
is connected to a generator which generates
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work out a electricity, and therefore, exhaust
kinetic energy is is basically considered
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as a loss. Therefore, in such a case, the
ideal turbine process would be isentropic
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such that there is no exhaust kinetic energy,
that is the exhaust itself is static and there
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is no kinetic energy associated with that
exhaust, and that is where we would define,
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what is known as Total-to-static efficiency.
In aero engines, the turbine exhaust is required
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to have certain amount of energy, which will
further be expanded in a nozzle to generate
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a thrust. So, there you would not want to
expand the turbine to such a level that it
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is static at the exit and very little kinetic
energy, but you would like that some more
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kinetic energy left, which can be expanded
further in a nozzle. So, there you would normally
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define the Total-to-total efficiency in such
applications. So, let us take a look at a
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general turbine process or expansion through
a turbine, and then we will come up with the
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efficiency definitions.
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So, this is an expansion process in a turbine
stage, while where station 1 is the nozzle
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entry, 2 is nozzle exit and 3 is the rotor
exit. So, 2 is also the rotor inlet. So, the
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flow initially has a pressure at the inlet
stagnation pressure at P 01 and static pressure
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the entry is P 1. So, P 01 plus P 1 plus the
dynamic head gives us P 01; so, we have plotted
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this on a temperature entropy scale. Now if
this entire process were to be isentropic
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then the expansion takes place along these
dotted lines. So, P 01 all the way up to the
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exit which is 3 s if it were if you are considering
a static condition at the exit and so, the
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actual turbine process of course, is define
by this solid line the bold line here between
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static pressure P 1, static pressure P 2 at
the nozzle exit or rotor entry and P 3 at
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the rotor exit.
The corresponding stagnation pressure at the
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rotor exit is P 03, which is basically what
you have the temperature at station 3 plus
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the dynamic head C 3 square by 2 C p will
give us the stagnation temperature there.
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Now, the corresponding conditions in the isentropic
case would be T 03 subscript s or at the rotor
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exit which is stagnation, and so, when we
are defining efficiency in two different ways
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that we are going to discuss about; let us
first take up the Total-to-static efficiency.
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Now, in this case, we are talking about an
ideal turbine work with no exhaust kinetic
23:38.390 --> 23:44.020
energy, which means that we have expanded
all the way up to the station, which is given
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by this particular stage. So, from 01 all
the way up to the station, and which means
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there is no more kinetic energy at the exit
of the turbine. So, we have the ideal turbine
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work in this case would be C p times T 01
minus T 3s.
23:58.880 --> 24:05.880
So, the Total-to-static efficiency in this
case is defined as the... it is denoted by
24:06.029 --> 24:13.029
symbol eta t as which is Total-to-static.
T 01 minus T 03 divided by T 01 minus T 3s
24:15.100 --> 24:22.100
that is T 01 minus the temperature corresponding
to this T 03 divided by T 01 minus T 3s. So,
24:24.100 --> 24:31.100
that is the Total-to-static efficiency. The
denominator we are going to simplify, because
24:31.470 --> 24:35.970
this is an isentropic temperature here; so
this can be expressed in terms of the corresponding
24:35.970 --> 24:42.529
pressure ratios, and so we have T 01 minus
T 03 at the numerator divided by T 01 into
24:42.529 --> 24:49.159
1 minus P 3 by P 01 raise to gamma minus 1
by gamma, this follows from the isentropic
24:49.159 --> 24:56.159
relation. So, this is basically 1 minus T
01 by T 03 divided by 1 minus P 3 by P 01
24:56.990 --> 25:03.840
raise to gamma minus 1 by gamma. So, this
is the basic definition of Total-to-static
25:03.840 --> 25:05.380
efficiency.
25:05.380 --> 25:11.570
Now if you look at an applications, typical
application being turbojet engine where the
25:11.570 --> 25:17.649
exhaust kinetic energy not really a loss,
it can be converted to thrust using a nozzle.
25:17.649 --> 25:23.890
So, in such cases, the ideal turbine work
is not equal to the static conditions at the
25:23.890 --> 25:29.850
exit, but the stagnation conditions. So, the
ideal work in such cases would be C p times
25:29.850 --> 25:36.850
T 01 minus T 03s and therefore, we define
Total-to-total efficiency which is eta t t
25:40.899 --> 25:47.899
that is T 01 minus T 03 divided by T 01 minus
T 03s and again the denominator we will express
25:48.390 --> 25:55.390
in terms of pressure ratios because of isentropic,
we have 1 minus T 03 by T 01 divided by 1
25:55.980 --> 26:00.770
minus P 03 by P 01 raise to gamma minus 1
by gamma.
26:00.770 --> 26:07.360
So, we have defined two forms of efficiencies,
the Total-to-static to static efficiency and
26:07.360 --> 26:12.830
Total-to-total efficiency; we can also now
relate these two types of efficiencies, and
26:12.830 --> 26:19.510
see how these efficiencies can be compared,
for the same type of... For the same configuration;
26:19.510 --> 26:24.830
if you were to compare these two different
forms of efficiency of course, with certain
26:24.830 --> 26:30.779
assumptions, we can still compare Total-to-static
efficiency and Total-to-total efficiency,
26:30.779 --> 26:37.779
and we will also see how using these efficiencies,
we can calculate work done by a given turbine.
26:38.070 --> 26:45.070
So, if we if we were to make an approximation
that T 03s minus T 3s is approximately equal
26:46.669 --> 26:53.669
to T 03s minus T 3 is equal to C 3 square
by 2 C p which is let me go back to the diagram
26:54.539 --> 27:01.539
here. So, what we are saying is the difference
between T 03 s minus T 3s and this and T 3
27:04.080 --> 27:11.080
s is C 3 square by 2 C p; so which means that
the effectively T 03s and T 3 they are not
27:11.240 --> 27:16.799
much different as you can see from this T-s
diagram itself. So, it is a very much a valid
27:16.799 --> 27:22.779
assumption that we can make, and so if this
this were to be the case, if you make this
27:22.779 --> 27:29.570
assumption, then we can relate Total-to-total
efficiency as equal to eta ts divided by 1
27:29.570 --> 27:35.360
minus C 3 square multiplied by 2 C p T 01
minus T 3s.
27:35.360 --> 27:41.740
So, what you can see here is that if this
assumptions were to be true, and you calculate
27:41.740 --> 27:48.460
the Total-to-total efficiency and Total-to-static
efficiency for a turbine, we could see that
27:48.460 --> 27:53.390
the Total-to-total efficiency is likely to
be greater than the Total-to-static efficiency
27:53.390 --> 27:59.990
which is also obvious from the T-s diagram
that I had shown; if you look at the expansion
27:59.990 --> 28:05.769
process for the same turbine, if you calculate
both these efficiencies, the Total-to-total
28:05.769 --> 28:12.000
efficiencies is likely to be higher than the
Total-to-static efficiency. Now, so using
28:12.000 --> 28:16.840
these definitions one can also calculate or
make use of these definitions to calculate
28:16.840 --> 28:22.269
the corresponding work done by the turbine
depending upon the application itself.
28:22.269 --> 28:28.480
So, if you were to use the Total-to-total
efficiency then we have the work done or specific
28:28.480 --> 28:35.480
work done as in case where let us say in an
application of gas turbine engine used in
28:36.679 --> 28:42.720
aero aircraft engine like an turbojet, then
the work done by the turbine is related to
28:42.720 --> 28:49.720
the efficiency, which is Total-to-total efficiency
multiplied by C p into T 01 into 1 minus P
28:50.679 --> 28:57.679
03 by P 01 raise to gamma minus 1 by gamma
and similarly, the work specific work related
28:58.700 --> 29:05.700
to the Total-to-static efficiency as eta t
as into C p T 01 one minus P 3 divided by
29:06.679 --> 29:13.679
P 01 raise to gamma minus 1 by gamma. So,
using the efficiency definitions and this
29:14.190 --> 29:20.370
specific applications for which these efficiencies
have been define for we can use this efficiencies
29:20.370 --> 29:27.370
to calculate the corresponding work done by
turbine the under this or different applications.
29:27.590 --> 29:32.250
So, let me give you one example to just indicate
the effect of reactions.
29:32.250 --> 29:38.590
I think, I have mentioned when I was talking
about impulse and reaction turbines that both
29:38.590 --> 29:42.380
these turbines in the last class, as well
as I mentioned that there is a difference
29:42.380 --> 29:48.820
in specific work done and loading that both
of these different types of turbines can handle,
29:48.820 --> 29:53.309
and also the fact that there is a certain
difference in the efficiencies that one would
29:53.309 --> 29:58.480
get by using these two different configuration
of turbines. So, let us take a look at the
29:58.480 --> 30:05.480
influence of loading on the efficiency, we
will in this case, calculate Total-to-static
30:05.710 --> 30:12.710
efficiency; So, you have reaction on the x
axis, the efficiency Total-to-static efficiency
30:13.799 --> 30:20.799
on the y axis and three different values of
loading. So, one can see that as you increase
30:21.409 --> 30:27.809
the loading and keep changing the reaction
what happens to the efficiency.
30:27.809 --> 30:33.659
So, let us take a look at one of these cases,
where let us say loading factor is equal to
30:33.659 --> 30:40.659
1. So, as you change the reaction on the extreme
right, we have an impulse turbine, which has
30:42.019 --> 30:49.019
a reaction of 0. So, as we start from an extreme,
which is an impulse and we move towards, let
30:51.570 --> 30:57.850
say a 50 percent reaction case, you can see
that there is a steady increase in the efficiency
30:57.850 --> 31:03.830
and after that of course, there is a drop
in the efficiency this is for loading factor
31:03.830 --> 31:09.480
is equal to 1.
Now, if you look at a loading factor greater
31:09.480 --> 31:15.289
than 1, let us say loading factor of 2 or
3, then the trends or slightly different;
31:15.289 --> 31:21.960
in fact, you get the highest efficiency when
the the reaction is equal to 0, that is for
31:21.960 --> 31:28.519
an impulse turbine stage, that is with higher
amounts of loading your impulse turbine stage
31:28.519 --> 31:34.899
as a better efficiency than any other case
of reaction, because the moment you have any
31:34.899 --> 31:40.389
amount of reaction it is no longer an impulse,
it it basically becomes a reaction turbine
31:40.389 --> 31:47.389
and that is also true for higher values of
loading between 2 and 3 and so on; and so,
31:48.600 --> 31:54.690
this is just to give some idea about what
happens as we change the amount of loading
31:54.690 --> 32:01.690
with increase levels of loading, how does
reaction influence the efficiency this is
32:01.850 --> 32:07.049
also linked to a comment add made earlier
I would want you to think about why is it
32:07.049 --> 32:12.730
that as you increase the loading, an impulse
turbine seems to at least perform better in
32:12.730 --> 32:19.730
terms of an efficiency, and what is the effect
of increase in loading on let us see the efficiency
32:20.360 --> 32:26.539
of the turbine as you keep changing the level
reaction from impulse which has 0 reaction;
32:26.539 --> 32:31.720
let us say to 50 percent reaction where the
reaction is the enthalpy drop is equally shared
32:31.720 --> 32:36.289
by the nozzle and the rotor.
So, just give it a thought on why there should
32:36.289 --> 32:43.289
be drop in efficiency, as you move from impulse
towards higher levels of reaction. So, let
32:43.769 --> 32:50.769
us move on to the next topic, we have for
discussion in today's class that is to do
32:51.840 --> 32:57.630
with losses in a turbine. I mentioned in the
beginning that I will restrict the discussion
32:57.630 --> 33:04.049
to just the basics of losses, because I already
had a detailed discussion on losses; when
33:04.049 --> 33:08.639
we are talking about compressors, and so most
of the concepts, we have discussed there is
33:08.639 --> 33:12.830
applicable for the turbine as well; of course,
the magnitude of the losses will be quite
33:12.830 --> 33:19.610
different for compressors and turbines, but
the concept is still the same. So, I will
33:19.610 --> 33:26.610
not repeat the estimation of losses that we
had discussed in detailed with reference to
33:26.639 --> 33:30.029
a compressor, because it is applicable for
a turbine.
33:30.029 --> 33:37.029
Now, when I discuss about compressors and
losses in a compressor, I had mentioned that
33:37.210 --> 33:42.450
there are distinct forms of losses. They are
basically we could classify losses as four
33:42.450 --> 33:48.139
sets of losses, one is on account of viscous
effect are known as the viscous losses ,then
33:48.139 --> 33:52.990
there are three-dimensional effect like tip
leakage flows and secondary flows; one may
33:52.990 --> 33:59.990
have shock losses and also mixing losses,
and so if you were to isolate these losses,
34:03.880 --> 34:09.490
because if you have to estimate losses in
a turbine and one would like to target, let
34:09.490 --> 34:15.250
us say different forms of these losses, and
see if we can minimize these losses, one would
34:15.250 --> 34:19.370
need to know, let us say what is contribution
of discuss loss, what is the contribution
34:19.370 --> 34:23.110
of 3-D losses like secondary flows or tip
leakage flows and so on.
34:23.110 --> 34:30.110
But, it is not very easy to segregate these
different losses. There are empirical correlations
34:30.440 --> 34:35.340
for estimating all these different forms of
losses; we had discussed some of them in in
34:35.340 --> 34:41.900
the context of compressors, one could extend
the same for turbines as well. Total losses
34:41.900 --> 34:46.590
in a turbine obviously, is the sum total of
all these different forms of losses, whether
34:46.590 --> 34:52.080
it is viscous loss or 3-D losses, which includes
secondary flows and tip leakage flows, shock
34:52.080 --> 34:55.560
losses and the mixing losses.
34:55.560 --> 35:02.560
So, let us look at these losses in little
more detail, but not too much as I had mentioned,
35:02.810 --> 35:09.140
some preliminary discussion on these losses;
if you look at viscous losses, there are again
35:09.140 --> 35:16.010
differ components of viscous losses; there
is one, on account of the profile or the nature
35:16.010 --> 35:21.450
of the airfoil cross section, and that is
known as the profile loss. Annulus loss would
35:21.450 --> 35:26.470
refer to growth of boundary layer along the
axis and end wall losses on account of boundary
35:26.470 --> 35:31.860
layer effects in the corner or junction between
the blade surface and the casing or hub. Now,
35:31.860 --> 35:38.860
in 3-D effects, we have a secondary flow which
is on account of flow through curved blade
35:38.880 --> 35:44.590
passages; tip leakage flows, which is basically
the flow leaking from the pressure surface
35:44.590 --> 35:51.590
to the suction surface, and what is generally
observed is that if you look at the 3-D effects,
35:52.180 --> 35:57.610
the losses are likely to be higher for the
turbine in primarily, because of the fact
35:57.610 --> 36:04.610
that the flow turning is much higher in a
turbine as compare to a compressor.
36:04.720 --> 36:10.130
Secondary flow for example, is directly related
to the amount of flow turning, and if you
36:10.130 --> 36:16.100
compare a compressor with that of a turbine,
the flow turning in a typical turbine blade
36:16.100 --> 36:22.540
is much higher than that of compressor. Secondary
flows are likely to be much higher in in the
36:22.540 --> 36:27.800
case of turbine; this is also true for the
tip leakage flows, basically, because tip
36:27.800 --> 36:33.560
leakage is on account of the difference between
the pressure surface and the suction surface
36:33.560 --> 36:39.880
and blade loading is usually much higher in
a turbine than in compressor and therefore,
36:39.880 --> 36:46.230
leakage flows are are also likely to be higher
in the in turbine and what complicate matter
36:46.230 --> 36:51.770
in a turbine is the fact that you also have
higher temperature, and it is no longer just
36:51.770 --> 36:56.400
for your air, you also have a combustion product
coming in from the combustion chamber which
36:56.400 --> 37:03.400
might complicate the flow behavior in the
case of a turbine. Now, let me just give you
37:04.640 --> 37:11.420
one example of profile loss, I will as I mentioned,
I am not going to details of estimating all
37:11.420 --> 37:15.970
these losses, we have done that for the compressor
and you could easily extend that to the turbine
37:15.970 --> 37:17.430
as well.
37:17.430 --> 37:24.430
Now, if you look at, let say the profile loss,
and look at what happens as you keep changing
37:25.080 --> 37:31.680
the incidence? Now, I have these profile loss
distribution for two distinct cases of impulse
37:31.680 --> 37:38.680
turbine and the reaction turbine. The solid
line refers to the impulse turbine, and the
37:40.430 --> 37:47.430
dotted line is for reaction turbine. So, one
can see that there is a significance difference
37:48.040 --> 37:53.390
between what happens in an impulse turbine
and reaction turbine, the losses as you can
37:53.390 --> 38:00.390
see are much higher for an impulse turbine
case and that vary significantly with the
38:00.850 --> 38:07.850
incidence. So, the sensitivity of impulse
blades to incidence is much higher, especially
38:09.560 --> 38:16.560
positive incidence, you can see that after
a round 8 or 9 degrees the losses increase
38:16.940 --> 38:21.590
substantially; there is a very sharp increase
in losses at positive incidence around 8 or
38:21.590 --> 38:28.280
9 degrees of course, this is for a very typical
case of a turbine blade; on the other hand,
38:28.280 --> 38:35.280
if you look at the reaction blade, it is properly
a little better adjusted to higher changes
38:35.530 --> 38:41.680
in incidence; of course, with very high incidence
exceeding 20 degrees, there is of course,
38:41.680 --> 38:46.770
very steam increase in the losses even in
a reaction stage, but if you look at the performance
38:46.770 --> 38:52.800
of a typical reaction blade it is not very
sensitive incidence between let us say plus
38:52.800 --> 38:59.800
minus 10 degrees, whereas an impulse blade
is quite sensitive to incidence and especially
39:02.500 --> 39:08.990
at positive incidence angles.
We also have alpha 2 plotted for both these
39:08.990 --> 39:15.990
cases, what we can see is that alpha 2 remains
more or less well behaved, whether it is impulse
39:16.010 --> 39:23.010
or reaction turbine. Even though the incidence
is different, the basic reason for this being
39:23.600 --> 39:29.720
true is the fact that in both impulse as well
as reaction blade the flow is encountering
39:29.720 --> 39:35.740
an accelerating flow a favorable pressure
gradient. So, even if there is higher level
39:35.740 --> 39:42.740
of incidence of the flow entering the nozzle,
because it is an accelerating flow the flow
39:43.190 --> 39:50.190
is generally well behaved, which is unlike
in a compressor where is the flow encounters
39:50.370 --> 39:56.500
an adverse presser gradient, and so the outflow
would be extremely sensitive to the in incidence
39:56.500 --> 40:02.930
angle as well that is if incidence varies
between a beyond a certain range the outflow
40:02.930 --> 40:08.870
angle also correspondingly changes drastically,
because of the fact that the flow is encountering
40:08.870 --> 40:14.430
and adverse pressure gradient and so, the
chances of flow separation is substantially
40:14.430 --> 40:21.430
higher, in in the case of a compressor which
is not true for a turbine where the flow is
40:21.580 --> 40:27.970
almost always encountering a favorable pressure
gradient and therefore, that partly explains
40:27.970 --> 40:34.970
why the gas outflow angle alpha 2 really does
not change much and the the insensitivity
40:35.240 --> 40:42.240
of outflow angle is larger much larger for
a turbine as compare to that of a compressor.
40:43.890 --> 40:50.890
Now, if you if you now, we come back to the
the types of losses in a turbine, if you recall
40:51.560 --> 40:58.170
when we discuss about losses in a compressor.
We had classified them into two distinct sets
40:58.170 --> 41:04.220
of losses, one is to do with 2-D losses and
one is to do the 3-D effects, like secondary
41:04.220 --> 41:11.220
flows and and so on. Now, if you look at just
the 2-D losses for which the lot of empirical
41:11.320 --> 41:14.090
correlations available.
41:14.090 --> 41:20.820
2-D losses basically are relevant to axial
flow turbo machines and you have seen that
41:20.820 --> 41:26.460
in a compressor as well as that when you are
discussing about axial compressors that if
41:26.460 --> 41:32.060
you if you look at 2-D losses, they are mainly
associated with the blade blade boundary layers,
41:32.060 --> 41:35.750
shock boundary-layer interactions, separated
flows and the wakes. some of these are of
41:35.750 --> 41:42.430
course, not really that significant for a
turbine for example, these separation or blade
41:42.430 --> 41:47.790
boundary layers, which are fairly well behaved
in the case of turbines and separation on
41:47.790 --> 41:53.630
the other hand; in in certain operating conditions,
one might have a lead leading edge separation
41:53.630 --> 42:00.630
bubble in the rotor, but that is the the chances
of such occurrence are very less there; unlike
42:03.930 --> 42:08.540
in the case of compressors where boundary
layer behavior is always a concerned because
42:08.540 --> 42:15.200
of pressure gradients.
So, mixing of these wakes that come from the
42:15.200 --> 42:22.010
rotor blade with the nozzle downstream of
the nozzle second next stage; obviously, creates
42:22.010 --> 42:26.220
a certain amount of losses and that is of
course, something that can be estimated by
42:26.220 --> 42:32.930
mixing loss models which are available from
which one can estimate to a certain amount
42:32.930 --> 42:39.720
of accuracy what is the effect of these wakes
shut from the rotor on subsequent stages.
42:39.720 --> 42:46.420
So, if we look at 2-D losses in particular,
we can classify two-dimensional losses into
42:46.420 --> 42:48.280
different forms.
42:48.280 --> 42:53.760
We have profile loss to tip the boundary layer
and its effect and whether you have laminar
42:53.760 --> 42:59.590
or boundary layer separation which is of course,
rather rare in the case of turbines, one may
42:59.590 --> 43:06.590
have wake mixing losses because of the wake
from the rotor interacting with the subsequent
43:06.770 --> 43:13.350
stages. One may also have shock losses, which
I will also discuss little more detail in
43:13.350 --> 43:19.100
the later slide and of course, the trailing
edge loss due to the blade because trailing
43:19.100 --> 43:25.080
edge is usually rounded as we have seen in
compressors, one may have to provide a certain
43:25.080 --> 43:30.340
rounding at the trailing edge there is certain
amount of loss associated with that rounding
43:30.340 --> 43:31.350
as well.
43:31.350 --> 43:36.720
So, the total a turbine like in the case of
compressor is obviously, a sum total of all
43:36.720 --> 43:43.280
these different components. So, without going
into details of how to estimate these losses,
43:43.280 --> 43:50.180
we can just summarize that the overall losses
in a turbine is a sum total of all these different
43:50.180 --> 43:57.180
forms losses. One may have profile loss on
account of the nature of the blade surface
43:57.390 --> 44:03.430
itself, one may have shock losses and secondary
flow losses which can be quite significant
44:03.430 --> 44:07.630
in turbines tip leakage loss and of course,
end wall losses.
44:07.630 --> 44:12.370
So, if you make of comparison of these with
a compressor, let us say a transonic compressor
44:12.370 --> 44:19.370
where also you may have a shock losses. The
major distinguishing factor between turbine
44:20.230 --> 44:25.600
and a compressor in terms of losses would
be the 3-D effects which are likely to be
44:25.600 --> 44:31.360
much more significant in a turbine like secondary
flows and tip leakage flows as compare to
44:31.360 --> 44:36.620
a compressor where of course, these losses
are still present, but if you were to make
44:36.620 --> 44:42.980
a one to one comparison The losses in in the
case of a turbine when it comes to secondary
44:42.980 --> 44:46.260
flows and tip leakage flows are likely to
be higher.
44:46.260 --> 44:51.030
But of course, there are methods of controlling
some of these in a turbine, because many of
44:51.030 --> 44:56.960
the turbine blades also have cooling mechanisms
which again we will discuss in detail in later
44:56.960 --> 45:02.840
lectures. So, some of these cooling holes
are also sometimes used to minimize let us
45:02.840 --> 45:07.910
say the tip leakage flows or secondary flows
in some way or the other, we will discuss
45:07.910 --> 45:10.850
that in in some of our later lectures.
45:10.850 --> 45:16.320
Now, there is another aspect, I wanted to
have some discussion on that is to do with
45:16.320 --> 45:23.320
deviation and I will probably spend a couple
of slides on this aspect as well. Now, this
45:24.320 --> 45:30.700
is also true with in the case of compressors,
and then it is an it is an own fact that when
45:30.700 --> 45:36.410
the flow exiting the rotor does not really
leave the blade at the angle for which it
45:36.410 --> 45:42.490
has been designed for. But it of course, in
the case of turbines it is the easier to estimate
45:42.490 --> 45:49.490
the out flow angle, because the flow is encountering
an accelerating flow passage and if the flow
45:52.240 --> 45:58.550
is not basically choked or if there are no
shocks present at the exit of the rotor, then
45:58.550 --> 46:04.720
it is the exit of the nozzle it is relatively
easier to estimate the amount of the outflow
46:04.720 --> 46:10.220
the gas outflow angle from the nozzle. But
of course, if there are shocks present that
46:10.220 --> 46:15.240
something which I will show you little later
then the outflow angle can be quite different
46:15.240 --> 46:21.160
from from what it has been basically designed
for. So, what what is basically found from
46:21.160 --> 46:27.420
experience is that the actual exit angle at
the design pressure ratio can be fairly well
46:27.420 --> 46:34.060
estimated by cos inverse of d by s as long
as the nozzle is not chopped.
46:34.060 --> 46:41.060
Let me just explain what I mean by cos inverse
of d by s. So, if you look at typical nozzle
46:41.310 --> 46:47.430
exit flow when I had shown a picture of the
cascade, I had mentioned that this is basically
46:47.430 --> 46:54.430
the throat of the nozzle and and the flow
exits the nozzle at an angle of alpha 2. So,
46:56.040 --> 47:02.150
if you look at the pitch at the trailing edge
which we have denoted by s and this is the
47:02.150 --> 47:09.150
throat and which is denoted by d, then one
can estimate the the outflow angle the gas
47:12.380 --> 47:19.240
out flow angle alpha 2 as what is shown here
that is cos inverse of d by s that is if you
47:19.240 --> 47:23.880
take an inverse of of course, that is still
an approximation, but it is found that it
47:23.880 --> 47:30.170
is fairly well the approximation fairly well
captures the at the angle at which flow exits
47:30.170 --> 47:37.170
the nozzle. Now, this is true as long as the
nozzle is not choked, because once it choked
47:39.780 --> 47:43.580
the nozzle is choked operating under choked
conditions then there is a possibility that
47:43.580 --> 47:50.490
at the outflow is supersonic which means that
there is a possibility of the presence of
47:50.490 --> 47:55.240
shocks at the exit or trailing edge of the
nozzle.
47:55.240 --> 48:01.530
Presence of shocks can deflect the flow and
causes certain amount of deviation and in
48:01.530 --> 48:08.530
such cases of course, you one cannot really
estimate the angle exiting the nozzle as cos
48:11.340 --> 48:18.340
inverse d by s. So, if you look at a case
where there is the flow is not choked it is
48:19.920 --> 48:25.220
unchoked, then is obviously, there is no the
flow is not supersonic at the exit of the
48:25.220 --> 48:32.220
nozzle, and which means that the flow angle
can be basically well estimated by just taking
48:32.970 --> 48:34.820
the inverse of d by s.
48:34.820 --> 48:40.410
Now, if you look at the other case where there
is a possibility of shock, in which case it
48:40.410 --> 48:46.830
is basically choked flow after the throat,
because it is if you let me take you back
48:46.830 --> 48:53.830
here. After the throat you may have an expansion
here which might cause the flow to become
48:54.010 --> 49:00.240
supersonic, if the back pressure is low enough,
then you may have it is basically acts like
49:00.240 --> 49:07.240
a converging diverging nozzle, and one may
have shocks emanating from downstream of the
49:07.280 --> 49:14.280
throat. If there is a trailing edge shock
exiting at the flow exiting the nozzle, then
49:15.900 --> 49:21.090
the presence of the shocks obviously, can
deflect the flow to differ angle. So, as you
49:21.090 --> 49:25.930
see here the flow is not really exiting at
an angle that it was design for the presence
49:25.930 --> 49:30.720
of the shocks, there is a trailing edge shock
or reattachment shock and so on; the presence
49:30.720 --> 49:36.610
of the series of shocks can cause the flow
to get deflected or deviated at an angle which
49:36.610 --> 49:40.100
is quite different from what it has been design
for.
49:40.100 --> 49:47.100
So, in such cases as what you see here the
angle alpha 2 is not well established or estimated
49:49.600 --> 49:55.670
by simply talking at d by cos inverse of d
by s; of course, there are also a empirical
49:55.670 --> 50:00.550
correlations in this case to estimate the
flow angle, because if you know the shock
50:00.550 --> 50:07.550
structure of the flow leaving the nozzle from
the analysis of the flow through these different
50:09.380 --> 50:15.150
shocks, one can sort of estimate what is the
angle at which the flow is leaving the nozzle,
50:15.150 --> 50:22.030
but that requires a much more complicated
analysis than simply taking considering just
50:22.030 --> 50:27.910
the geometric parameters and estimating the
exit flow angle to be a function of these
50:27.910 --> 50:32.450
geometric parameters.
So, in the presence of supersonic flow where
50:32.450 --> 50:37.000
there are shocks present, the flow structure
is obviously, more complicated, and the flow
50:37.000 --> 50:42.590
undergoes deviation, which is more quite different
from what one can otherwise easily estimate.
50:42.590 --> 50:49.590
So, I just brought up this aspect of deviation,
because of the fact that in nozzle flow there
50:51.970 --> 50:58.160
is a possibility that the flow exiting nozzle
can be supersonic, and therefore, the flow
50:58.160 --> 51:03.980
might undergo a deviation which is quite different
from what is has been primarily design for
51:03.980 --> 51:10.980
which means that this flow entering into the
rotor basically has a different angle than
51:11.300 --> 51:16.930
what is been design for and therefore, one
needs to construct this aspect into account
51:16.930 --> 51:22.450
when estimating the flow through the entire
stage.
51:22.450 --> 51:27.710
Let me now quickly recap our discussion in
today's class; we had discussion on three
51:27.710 --> 51:34.710
distinct topics; We started off with degree
of reaction, and I spent some time discussing
51:34.810 --> 51:40.150
about degree of reaction it significance,
and how one can estimate degree of reaction
51:40.150 --> 51:45.990
and based on this estimation, how one can
determine the configuration of the turbine
51:45.990 --> 51:51.360
whether it is in impulse or reaction and so
on; we then spend some time discussing about
51:51.360 --> 51:58.360
losses the different type of losses the 2-D
losses and 3-D losses, and I mentioned that
51:58.520 --> 52:04.950
there are certain aspects of losses which
or the contribution of these different sources
52:04.950 --> 52:10.340
of losses is different in the case of turbine
and a compressor, because of the very nature
52:10.340 --> 52:17.340
of flow passing through a turbine or compressor.
We also discussed about the efficiencies and
52:18.060 --> 52:24.080
different definitions of efficiency, the Total-to-static
efficiency and the Total-to-total efficiency,
52:24.080 --> 52:29.770
which is what we discussed in detail today
and of course, towards end; I also discussed
52:29.770 --> 52:36.560
about the aspect of deviation, which is of
significance especially, when the flow is
52:36.560 --> 52:42.170
unchoked, and especially when the flow is
choked, and the flow exiting the nozzle is
52:42.170 --> 52:43.060
supersonic.
52:43.060 --> 52:49.910
We will continue our discussion on axial flow
turbines in the next lecture, we will basically
52:49.910 --> 52:56.750
be talking the performance characteristics
of an axial flow turbine, and how one can
52:56.750 --> 53:02.660
match the exit flow from a turbine with a
downstream component like a nozzle. So these
53:02.660 --> 53:07.570
are two aspects that we will be discussing
in the next lecture, which would be lecture
53:07.570 --> 53:08.450
number 22.