We are talking about axial flow turbines.
An axial flow turbine theory is the two
dimensional theories, the three dimensional
theories and a little good exposure to blade
cooling that we have done in the earlier few
lecturers. Earlier lectures have exposed you
to the general technology and the aerodynamic
theories behind the axial flow turbine
operations.
Now, in today's lecture we will start with
a discussion on how such axial flow turbine
blades are indeed designed. Now, axial flow
turbine blades just like axial flow
compressors are essentially aerodynamic machines.
So, the fundamental principle based on which
they operate are aerodynamic principles.
We have also seen that just like compressors,
the turbines essentially operate with
airfoils as the fundamental building block.
So, we need some kind of airfoils, to initiate
the aerodynamic activity which prompts the
turbine to work, and in this case actually
produce work compressors where work
absorbers turbines are work producers.
Now, in case of compressors we use one kind
of airfoils to put in work in the fluid. In
case of turbines, we use another kind of airfoil
to take out work out of the turbines. There
are one or two examples you know, just one
or two rare ones, where one can probably
use very similar or almost same airfoil for
both compressor and turbine. But, by and
large, airfoils that used for turbine are
significantly different from those used in
compressors.
We shall also look at how the overall turbine
blade is built up which we shall do in the
next class. The three dimensional shape, we
have seen that the compressor blades tend
to
be highly twisted and of course, they have
very complex shapes sometimes. We have
seen the basic design theory of turbine which
often differ from the basic compressor
design theories. In the sense, free vortex
is not the most popular theory for turbine
design
or for that matter near free vortex. The turbine
designers use here somewhat different
theory like a constant stator exit angle alpha
2 from root to tip.
So, the basic design philosophy of turbines
is also quite often different. Today we will
look at the basic airfoil that have deployed
in turbine and how those airfoils are indeed
selected or designed or created to put in
turbine blades. And of course, we have two
sets
of blades, we have the stators or stator nozzles
as we call them, and we have the rotors
which of course do the work.
So, we will look at various kinds of airfoils
including transonic and even supersonic
airfoils which have been used not necessarily
in the commercial aero engines. But, in
very special cases of turbines, gas turbines
are supersonic blade profiles have been used
and we will have a look at those. When we
discuss those things, we will have a brief
discussion on where and how those kind of
blades are probably actually utilized.
So, in today's lecture we will be looking
at axial flow turbine blade profiles. Now,
designing the blade profiles is one of the
issues that need to be looked at from a number
of points of view. One of the points of view
is that in the early days of design, the
profiles were generated by various NASA or
you know earlier Naka or various
laboratories in various countries in England
or in Germany or in Russia. There is various
design bureaus mainly set up by government
or respective governments and they created
some families of airfoils which were used
for compressors and for turbines rotors and
stators.
However, later on people have realized over
the years that what you need to do is not
necessarily use the same airfoils again and
again, but, you can indeed generate your own
airfoils to suit your own needs.
This of course, has brought in a lot of refinement
and it allows the efficiencies of the
turbines flow over the turbines to be very
accurately predicted and accurately reflected
in
the design. This allows for very high efficiency
turbine design in the modern gas turbine
engines.
These of course, use the modern computational
fluid dynamic techniques some of which
we will discuss briefly in the final lectures
of this lecture series. But, I will have a
very
brief mention of that in today's lecture just
to complete the profile design discussion
that
we having today. This tells us that profiling
today is not just a selection of a blade from
a
library or a catalogue, but, it is far more
involved and probably requires a little more
effort on the part of the designer to mesh
or to work with the analysts who are probably
the c f d people. Again you get into as we
have done in case of axial flow compressors,
you get into a design c f d analysis loop
and this is inevitable in the modern blade
design.
So, that is something which will very briefly
touch upon today, but, we will discuss in
some detail later on in this lecture series.
So, we will start off with blade design and
axial flow turbine blade profiles. Now these
profiles as we know are made up of airfoils.
So, the classical airfoils that people have
used over the years are based on basic design
philosophy.
Now, let us look at the basic design steps
or design philosophy that one starts off or
that
kick starts the design.
So, the first thing that you need to do is
selection of your design point. Now this
normally comes from the engine cycle. Engine
cycle is the first thing that must have
been designed and from which you have a design
point selection which tells us at what
altitude and what flying condition or what
ambient condition taken everything into
account the design is supposed to be made.
As we have seen before, you may have a
design point which is ground static or you
may have a design point which is flying,
which is typically used for supersonic aircraft
engines and in which case the design point
would indeed decide the number of starting
parameters. Now these starting parameters
are given in number two. One of the things
you would need to have of course, at the
design point is the turbine pressure ratio
or pressure drop across the turbine. Then
you
need to have the mass flow through the turbine
which is given as m dot gas and then of
course, the maximum diameter that is permissible.
This is indeed crucial if you are
having to design for a military engine where
the maximum diameter is definitely
restricted by the size of the aircraft itself.
Then of course, the turbine entry temperature
t
gas are what in cycle analysis one would call
t 0 3 or even turbine discussion we have
often called it t 0 3 or t 0 1 whichever way
you look at it. So, that is T gas.
Now, that gas temperature comes from combustion
chamber and you need to have an
idea what gas temperature you are letting
out into the turbines. So, depending on which
stage of turbine you are embarking on, you
need to decide the entry temperature to that
particular stage of turbine. If it is starting
off with a multistage turbine, the first stage
entry temperature needs to be decided which
of course, is coming from combustion
chamber. Now this is something which is normally
decided by the state of art of the
turbine material, and the turbine cooling
technology. As we have discussed in the cooling
lectures, this temperature has been pushed
upwards are very significantly by the cooling
technology from about 1000 k to presently
about 18 100 and 19 100 k.
So, turbine entry temperature as written here
as t g or t gas, is indeed decided by the
state
of art of technology of turbine blades. Then
of course, the ambient pressure and ambient
temperature which is decided by the flight
condition or if it is a land based gas turbine
it
is decided by the ambient condition at which
this engine is indeed going to be operated.
Now, this together constitutes the design
point. We know very well that the pressure
ratio pi 0 t or total temperature (total pressure
ratio as we call it) is indeed decided upon
after bit of a matching with the compressors.
Now, this matching is something which which
is a different you know topic altogether.
We have touched upon it a little earlier,
but, the more comprehensive part of it is
not
really inside the scope of this lecture series.
Somewhere you know, as you are aware I
mentioned should be just touched on a little
that you need to match your turbine with
your compressor.
So, the matched turbine pressure ratio which
also gives a matched compressor pressure
ratio needs to be arrived at at the design
point. So, you do not decide on a turbine
pressure ratio independent of the compressor
or the fan. You need to decide upon that
after doing a matching exercise.
So, this matching is something which is an
independent exercise by itself and one needs
to do that. Maybe some other group of people
would do that and then pass on the
matched value of the turbine pressure ratio
to the turbine designer and matched value
of
the compressor pressure ratio to the compressor
designer.
So, that is an exercise which is an independent
exercise and needs to be done at this stage
before the design is indeed embarked on. So,
that pressure ratio comes from an exercise
which includes matching of the compressor
and turbine or any other load that the turbine
is actually catering into. Then of course,
you have a number of parameters that you have
discussed in great detail in the earlier lectures.
One is at the stage loading coefficient,
which is normally in most textbooks and as
we have mentioned is psi and that is equal
to
the work done delta h divided by normally
half flow u square. In many books, the u is
normally the u mean square, but, in many actual
applications, people often use U tip
square. That means the tip U or the tip blade
velocity of the particular turbine rho of
course, is the entry density of the gas that
is passing through the turbine. delta h of
course, is the total work done in terms of
total parameters. Now this is the stage loading
coefficient which is normally used in most
stage characterization and it goes with the
flow coefficient phi which is simply C a by
U mean. Sometimes in various real
applications by various companies, the phi
is also mentioned as C a by U tip.
So, instead of U mean many people use U tip
as the normalizing parameter both for psi
as well as phi. Then of course, as you know,
the turbine is typically characterized by
the
so called psi phi diagram.
We have done that for compressors also if
you remember, same thing is done for turbine.
Of course, we can have regular mass flow versus
pressure ratio characterization which
also we have done in this lecture series.
So, the characterization of pressure ratio
versus
mass flow or the psi phi characterization,
both are valid characterizing of working
turbines. Both are useful for turbine operation
as well as indeed remember a very
important issue turbine controls.
So, we need to get the psi and phi values
first at the design point. Next thing we need
is
the degree of reaction. Now if you look at
the degree of reaction, again you would have
a
degree of reaction first at the mean. Then
of course, it will vary from the hub to tip.
Typically, it would vary quite a lot may not
be as much as an axial flow compressors,
but, would very still substantially from hub
to tip. Then of course, you need to decide
what the value of degree of reaction should
be. As you know, in case of an impulse
turbine, the degree of reaction indeed would
be 0; that means, all the static changes occur
in stator and no static change occurs in the
rotor.
On the other hand, most gas turbines that
we are dealing with are reaction turbines.
So,
they have a positive reaction value which
as I mentioned vary from root to the tip of
the
rotor or the inner diameter to the outer diameter
of the annular space of the turbine. The
next thing you need to decide is a blade flow
turning, first in the rotor and of course,
in
the stator. Now the rotor of course, gives
you the work done.
So, delta b is directly indicative of the
amount of work that you can accomplish out
of
this rotor. Corresponding delta alpha that
you get in stator would indicate the amount
of
turning that is necessary in the stator. That
turning of course, is sometimes inevitable
or
necessary to affect certain amount of change
of energy from potential to kinetic.
So, the blade flow turning in rotor for work
done in stator for change of energy are
vitally important things. Again, these would
be variable from root to tip. Now in case
of
stator, in many designs, it may be constant
from root to tip. But, in the rotor, it would
vary from root to tip which means the turbine
rotors would have some amount of twist.
Then you have the velocity triangles of the
angles and the velocities alpha 1, alpha 2,
alpha 3 and then beta 1 and beta 2 and beta
3 across the rotor corresponding velocity
C 1
C 2 C 3 and then the relative velocities V
2 and V 3 across the rotor. This would be
first
done at the mean. That is where the design
needs to be first, you know, initiated. Once
you have a design at the mean and you think
that this design would hold water and would
accomplish the amount of work that you would
like to do as mean, as a representative of
the entire turbine, then you can sit down
and do a variation from root to tip, which
means
all these parameter that we are talking about
indeed would vary from root to tip.
So, variation from root to tip is a separate
exercise. We will have a look at that variation
in the next lecture in which we deal with
the three dimensional blade design.
In today's lecture, we are dealing essentially
with the two dimensional aspect of the blade
design. So, first we will look at this mean
diameter issues. So, that it facilitates or
allows
us to do a mean diameter design. Indeed in
a multistage configuration, all the mean
diameters or mean of the blade or design,
first of all, the stages stator rotor stator
rotor
stator rotor of all the stages before any
of the stages take up hub to tip a detailed
design
or the 3D design.
So, the mean diameter design that we are discussing
the two dimensional design is
indeed the starting of all designs both in
case of turbine as we have done earlier in
case
of compressor. So, this is the way you initiate
the turbine design.
Let us take a look at some of the selection
criteria. Now the design requirements are
normally put in terms of the turbine efficiency
which is decided by the state of art of
design. It is decided by the the star represent
the design value the T star of the gas. The
maximum that can be allowed is decided by
the turbine blade technology which includes
the cooling technology. The materials science
and the metallurgy, all of it put together
decide what the turbine entry temperature
should be at the design point which is
normally one of the highest temperatures.
One would not advocate use of the turbine
of this turbine at a temperature much higher
than this. Maybe a few degrees higher would
be all right, but, substantially higher
temperature would be absolutely prohibited
once this design temperature has been
selected and the design has been made according
to the selection. So, turbine entry
temperature is the highest temperature in
the engine and that is decided after a lot
of
technology search and then once that is decided
at no point of time the engine should
work beyond this temperature level.
And then of course, the exit flow angle. Now
exit flow angle of turbine is important
especially if you have a nozzle as you have
in aero engines. The nozzle of course, creates
or helps create maximize the thrust that is
indeed required for flying of the aircraft.
Now, in the process of creation of thrust
what you require is a straight jet which means
exit flow angle from the turbine should be
0. The floor should go out straight and go
straight into the nozzle and go out straight
actually. That is when you have the
maximization of your thrust creation. If you
create turbine exit flow, which is a whirl
inflow that whirl component of the flow is
of no use as far as thrust creation is
concerned.
So, for thrust creation you need a straight
jet; no whirl component. Any whirl
component, even a 5 degree 10 degree alpha
value at the exit of the turbine would have
whirl component which is useless and is a
wastage of energy as far as thrust creation
is
concerned through the nozzle.
So, if you have a nozzle immediately after
the turbine that is deployed essentially for
creation of thrust, you would be asked to
design a turbine where the last turbine exit
angle is 0. So, that is a requirement which
is often imposed by the engine designer.
Then of course, the Mach number. The Mach
number from the turbine exit is important
if it is going again into the nozzle. If it
is going into the nozzle, (( )) probably going
to
make the nozzle supersonic or just sonic,
which means it may be a convergent nozzle
or
it may be a convergent divergent nozzle. If
it is a convergent nozzle, you were just going
sonic. It is important what is the Mach number
at which you are starting the nozzle flow,
which means, what is the Mach number with
which the flow is coming out of the turbine.
The other parameter that is important always
that cycle designer would have taken care
of is a pressure with which the flow is coming
out of the turbine.
So, the exit pressure from the turbine and
the exit Mach number from the turbine would
decide how the nozzle would perform thereafter
in an aero engine. If it does not have a
nozzle, as let us say, in a turbo shaft engine
or in land based gas turbine engines in which
case you do not have a nozzle. So, the exhaust
energy is not going to be used for creation
of thrust or anything. In which case, certain
amount of whirl flow may be you know
admitted, which means, there is a relaxation
on the turbine design. You see the alpha 2
exit or alpha exit at the n puts a restriction
on the turbine design or turbine designer.
So, if that restriction is relaxed, maybe
you can have a better turbine or a turbine
with
higher performance. So, these are requirement
which are often put on the turbine
designer and turbine designer would have to
abide by these requirements, in addition to
the constraints. Now let us look at the constraints.
Now, the constraints do apply for both high
pressure turbine as well as for low pressure
turbine. You have constraints on the turbine
rotating speeds rpms n 1 and n 2, then that
gives rise to the blade speeds U m one which
is mean U and mean diameter and then of
the HPT and then U mean to a diameter mean
of the LPT 2 represents here LPT 1
represent here HPT, and n 1 of course, is
a JPT and n 2 is LPT.
So, one here represents HPT two represents
LPT. So, the n U and D values need to be
decided upon based on the constraints. You
may have a stress limit constraint, the
compound stress limit which puts a limit on
the rotating speed corresponding limit on
the
blade speed and corresponding limit on the
blade size of the diameter of the blade. All
of
them to put together essentially put a some
kind of a constraints on the stresses that
come
on the turbine which when compounded with
the thermal stresses indeed put a huge
stress constraint on the turbine blades. This
is a constraint that comes from the structure
designer of the turbine blades, which is a
huge field by itself. Remember there are
thermal stresses even in LPT where you do
not have cooling.
So, the high temperature and high blade loading
creates huge load constraints. Those
constraints are passed onto the turbine blade
designer in terms of n U and D. He has to
abide by these constraints. He cannot go beyond
these constraints because those are huge
constraints based on turbine loading and those
loads put a restriction on the turbine life.
So, the life of the turbine is indeed in jeopardy.
So, turbine designer has to abide by these
limits. Then you of course, have the blade
and the disc stress levels. Now the disc stress
level is again a huge problem. Discs like
the blades are also made up of high temperature
materials. So, even if they are made of high
temperature nickel alloys, the stress levels
are indeed very stringent.
And there is high temperature all over the
place. So, that needs to be factored into
the
design. The first three parameters n u and
d actually come out of the next 3 parameters
that we were looking at the blade disc stress
levels. The materials technology which is
decided by the materials engineer, the material
science people and then of course, the
blade cooling technology decided by the cooling
technologies. We have discussed that in
the earlier few lectures. It is a huge field
by itself, a fascinating field by itself and
they
put a few restrictions on the turbine blade
designer. You have to abide by those
restrictions when you embark on your design.
Having decided or have not discussed, these
issues of requirements on one hand,
constraints on the other hand, let us start
with the blade profiles. What kind of blade
profiles are normally used in axial flow turbines?
The most classical airfoil design that is
normally used in gas turbines is the T 6 airfoil
which is normally used in many of the early
gas turbine blades.
Profile that is being shown here is a symmetrical
version of the basic blade profile that is
normally used in axial flow gas turbines.
This profile T 6 profile, there is another
one
which is famous one. T 1 0 6 which is normally
used in low pressure turbine and T 6 is
normally used in high pressure turbine.
Now, this profile is a symmetrical profile
as you were looking at. This profile is normally
bent. The amount of bent that you would like
to do is, typically decided by the designer.
The same profile may be bent by 90 degree
or it may be bent by 100 degree or even by
120 or 130 degree.
So, those decisions are taken by the turbine
designer. In the early days of turbine design,
this particular profile has been used again
and again with various bents. So, the bents
or
the camber is a separate issue. Quite often
you may have a circular arc camber or any
other arc camber, may even parabolic arc camber
with a total camber of the order of 92
120 130 degrees. We have discussed that in
case of turbine that camber is far higher
quite often thrice that of a typical compressor
camber.
So, that camber on which this blade profile
is distributed on. So, this thickness
distribution that you are looking at, it is
available in many literatures very easily
and that
thickness distribution is distributed over
the camber.
And then, you have a new profile. So, once
you distributed over different cambers you
have a completely new blade profile. Such
a blade profile has been used in many of the
turbines in the many of the earlier turbine
designs.
As I mentioned, there is another profile called
T 1 0 6 which has been used again for
many low pressure turbine usages. Of course,
we are showing you here which is a 10
percent thick turbine profile. One can have
even thicker ones, up to 20 percent which
is
been used in in rotors. Slightly thinner one
here are normally used in stators and thicker
ones are actually used in rotors.
Whereas in case of a particular rotor, actually
the amount of camber may vary from root
to tip. So, you may use the same profile,
but, with different camber from root to tip.
So,
some of those things we will look at in the
next lecture. So, this is the basic profile
on
which many of the early turbines have been
actually designed upon. If you have this
basic profile, how do you create the particular
configuration?
Now if you look at this diagram, you would
need to bend that profile to create this blade
or blade section. You would need to conform
to the fact that it is coming in with a
velocity V 2 let us say this is for a rotor.
It is coming in with a certain relative velocity
V
2 now. It is set at an angle beta 2 which
is what it would feel as the flow is coming
in and
then you would have to decide on the angle
of incidence.
Now, angle of incidence something which we
have discussed earlier is typically the
angle subtended by the tangent to the camber
at the leading edge to the flow direction.
So, the flow direction makes an angle of incidence
I with the tangent to the camber at the
leading edge. So, that tangent to the camber
is the angle at which the blade is set and
that
is beta 2. Now beta 2 is the ideal flow angle
with which the flow is supposed to be
coming for which the incidence would be 0.
However, most designers often prefer to have
a very small angle of incidence often a
positive 1 to facilitate that the blade loading
is always good blade loading. As you know
at a negative angle of incidence, the blade
loading indeed would go down.
The next issue is of course, at the exit,
where the flow is supposed to be going out
with
an angle beta 3 which is the exit angle. You
would indeed possibly have a very small
deviation or flow turning that is slightly
different from beta 2 plus beta 3. Now beta
2
plus beta 3 is indeed the flow turning here.
That as we can see could be very high of the
order of 100 degrees or so or even more.
That needs to be catered to with the shape.
In the process, it is entirely possible that
and
we shall see that the flow may not stick to
right up to the trailing edge. There may be
very small deviation much less than what we
have seen in case of compressors and quite
often it is a very small amount.
Then of course, you have to decide fundamental
airfoil parameters. The chord of the
airfoil which is absolute value of the chord
is decided by a number of considerations
indeed what should be the surface area of
this surface and surface area of this to allow
for sufficient contact between the blade surface
and the gas which is passing through.
That contact as you know of course, transfers
the energy from the gas to the blade.
So, there has to be a sufficient contact on
the surface between the gas and the solid
body
of the blade for effecting the work transfer.
So, that is an absolute amount that has to
be
decided by the designer what should be the
chord because that chord will decide the
surface area of contact between the blade
and the gas. This is decided by a lot of
calculations of the energy that is to be transferred.
Now, once you have decided on the chord and
you have some idea what beta 2 plus beta
3; that means the blade camber. You need to
decide on the two surfaces. You have a
radius of curvature of one surface and then
you have a radius of curvature of the other
surface. That means both the surfaces; the
pressure surface and the suction surface are
indeed actually circular arcs.
Many modern designers as we shall see later
on do are not necessarily stick to the
circular arcs. They often devise different
curvatures not necessarily circular. These
blades in the classical design, the circular
arc is followed by normally a straight line
on
both the surfaces and then a little rounding
at the trailing edge and then rounded at the
leading edge.
In many of the modern design, the rounding
at the leading edge is very prominent or very
large essentially to cater to the cooling
technology to be embedded inside it. So, many
of
the modern designs, accommodate a very large
rounded leading edge as we have seen in
the last lecture on blade cooling. That incorporates
or has embedded cooling technology
inside that rounded leading edge. Now, rounded
leading edge aero dynamically is
actually a compromise.
It is a sacrifice because more the rounded
leading edge; that means, more the leading
edge radius more would be the basic aerodynamic
penalty in terms of profile loss of the
airfoil. This is known. This is very well
known.
So, the aerodynamicist often does a little
bit of sacrifice in the aerodynamic penalty
or
loss to accommodate blade cooling technology
inside the blade. This is typically
necessary for high pressure turbine HPT plates
because you need cooling there.
So, many of the HPT blades would have much
more rounded leading edge whereas, the
LPTs may not have that rounded leading edge
because quite often LPT or the last few
turbines specially do not have any cooling
technology embedded inside.
And then of course, you need to decide on
the opening or more specifically the throat
of
the turbine passage. Now, the flow coming
through this passage typically would have
a
converging curve passage and it would indeed
have the minimum area over here at this
opening which is often the throat of the passage.
Now, throat of the passage is of course, the
constriction or the restrictions on which
the
blades are deliberately designed to create
an expanding flow or an accelerating flow
over
this blade profile. Now what happens is this
opening is decided by also the pitch.
We shall discuss how to decide on the pitch
again later on. More spacing you provide;
that means, more apart the blades are you
have a lesser and lesser surface friction
related
losses. On the other hand, more closer they
are in terms of spacing you would actually
have more and more surface friction losses.
But, you are going to have more and more
turbine work transfer.
So, more apart they are normally, the losses
are less. Primary losses, the surface friction
losses, less closely they are packed more
you have the losses. But, you have better
presumably and definitely calculable better
performance features.
So, it is a slight you know tug of war or
a compromise between more work that can be
accomplished probably with efficiency penalty.
In other case, where you have higher
efficiency probably you are going to get less
work done. So, this compromise is what the
designer would have to decide upon early on
during the design process. So, these are the
basic flow parameters and then we start off
with the geometrical parameters.
If we carry on with the geometric parameters,
we see that this is the stator. The earlier
one we were looking at was a rotor. Now this
is the stator where your entry angle is
typically given in terms of alpha. Typically,
you are likely to have a rounded leading
edge. This is what I was talking about that
you have more rounded leading edge for
typical stator because a stator is likely
to be cooled. Even some of the early LPT stator
may be cooled. Rotors may not be cooled. HPT
of course, rotor and stator both are cool.
Now, you can see here that the radius of curvature
that you give to a typical stator blade
it is circular around this area. Whereas,
it is unlikely to be a circular all over.
So, you
have a circular arc starting early on, maybe
very close near the leading edge. Then you
have a circular arc and then from here onwards,
you probably have a straight line, more
or less straight line over here.
So, you have a circular arc over here and
then you have another circular arc over here.
This is the radius of curvature or radius
of the circular arc. This is the radius of
this
circular arc and typically they end up with
straight lines over here. Then, at trailing
edge
rounding, typically given in terms of trailing
edge radius. So, you have a number of
geometrical parameters to be decided upon.
Now this throat area is very important for
stator design because in many stators, that
throat is likely to provide sonic flow and
that
is related to the blade pitch that you are
getting. Of course, if the pitch is more throat
is
going to open up.
So, it is given here in terms of o is equal
to s into tan alpha 2. alpha 2 is angle with
which
the flow is indeed coming out. This is decided
often by now if you have 90 degree over
here, it means that the flow will actually
be not tan alpha but it will be sin alpha.
If this
angle is 90 degree then of course, o is s
tan alpha.
So, depends on whether by design this angle
is 90 degree or this angle is 90 degree.
Many designers would like to have this as
90 degree because this is a straight line.
Some
would like to have this as 90 degree. Of course,
this is always a straight line.
So, it depends on the designer and depending
on that, o is the throat area is decided upon.
Then, of course, the t by c, the ratio, the
the thickness which is decided. We saw the
t by
c ratio of the t 6 blade which was 10 percent
here we see it is given as 20 percent.
Then, of course, the various other parameters
such as the spacing to radius of the trailing
edge and then spacing to trailing edge radius
which is given as 0 2. Some of these ratios
in terms of trailing edge radius, in terms
of the chord or the geometrical parameters
that
the turbine designer would have to finally
carry out before it is given for analysis
and
then later on for fabrication. So, these are
the geometric modelling issues that the turbine
designer would have to decide up on.
This is a picture that tries to capture everything
that the turbine indeed has. You have to
begin with, which are decided upon the throat
area which is typically done by actually
drawing a circle over here. Then of course,
the inlet flow angle coming in beta 1, exit
flow angle beta 2 as I mentioned, you can
have a small deviation flow. Deviation over
here which means the floor does not quite
actually cater to either beta 2 or alpha 2
which
would be in case of a stator. Then of course,
depending on the chord you decide upon the
blade stagger angle. So, this is your blade
chord and that is your blade stagger angle
angle it makes with the axial direction.
So, that is your blade stagger or blade setting
or blade fixing angle as the assembly
people would call it. So, you would need to
decide on those things. As you can see here,
the blade stagger angle really speaking has
nothing much to do with the aerodynamics of
the flow. It is really necessary for blade
fixing and setting of the blade. Because,
the huge
camber that turbine design blades normally
carried by design actually sets it apart from
the chord direction of the chord. As a result
of which, it is really nothing to do with
the
blade setting angle. But, at the end of the
day you have to provide the blade setting
angle
by design because the blade will be actually
fix there at the time of assembly.
Then of course, this is your flow deflection
beta 1 by minus beta plus beta 2 or alpha
1
plus alpha 2. Then of course, these are the
tangents to the camber line. So, this is one
tangent, this is another tangent and the angle
between the two is the blade camber.
So, blade cambers are decided by the tangent
to the camber line at the leading edge and
at the trailing edge. Incidence is decided
by the flow direction with the tangent to
the
chamber at the leading edge. The deviation
is decided by the flow direction with the
tangent to the camber at the trailing edge.
So, all those things geometrical as well as
flow parameter of fluid dynamic gas dynamic
parameters are put together in this diagram.
It captures almost everything that is
necessary for the turbine designer to decide
upon. All these parameters would have to be
decided by design. None of it can be left
out. All these parameters would need to be
decided upon by design.
Now, this is what the turbine designer would
be looking at. You have the pressure
surface cp distribution and one is the ideal
one which you start off with. Then of course,
you make small changes in the modern design.
You make the changes with the help of
CFD and you may get final cp distribution
which is something like this. What I show
here is static pressure by total pressure
similar to cp and it shows that it does not
follow a
smooth curve than a small thing over here.
Then there is small prominent recompression;
that means, a small diffusion of the flow
before it hits the trailing edge of the suction
surface. So, this is done deliberately to
deviate from the ideal starting profile to
arrive at
a final profile.
This is what is at typically done for a stator.
Typically profile needs to be decided or
designed in a cascade form. He does not decide
an airfoil form. It is in a cascade form
with all those spacing and other parameters
in place. Only then you know the cp
distribution. The cp in cascade is quite different
from the cp in actual single airfoil.
So, you need to have the cascade static pressure
to total pressure distribution decided
upon. This is your pressure surface and this
is your suction surface and at the exit you
may have some slight things over here and
finally, of course, they have to match.
In this particular case for example, we see
that the exit Mach number here could be as
high as 1.2 to 2 which means it is going out
supersonically. Its going out entry is .2.
So,
it has accelerated from M 1 2 to M 2 1 to
2.2. A huge acceleration has taken place over
this blade passage and as you can say there
is a huge convergence of the blade passage
which gives rise to these huge expansion or
acceleration.
This is a picture of a rotor where as you
can well imagine, the acceleration is not
as much
as in the stator. The flow comes in with a
Mach number relative Mach number .61. Part
goes out with a Mach number which may be slightly
or marginally supersonic.
It comes in with an angle of 35 goes on with
an angle 29. So, beta 1 plus beta 2 would
be
the turning angle and the turning angle that
is shown here is not necessarily very high.
You can have rotors that have turning angles
even higher than that. But, in gas turbines
as we have discussed before in quite a detail
that the turbine rotor design does not
depend entirely on the turning, it depends
also on the reaction. So, acceleration that
is
taking place would give you the reaction which
will give you the additional work that is
accomplished by this particular rotor. One
can see that finally, experiments have been
done in cascade tunnel to match the experimental
values with the design values.
So, that you are assure that you have a reasonable
matching between what you have
design and what you are likely to accomplish
in actual blades.
T
This is what happens when you have turbine
blade. What is shown here is the pressure
loss. You remember pressure loss is what gives
rise to the efficiency penalty and as you
can see here if the flow is turbulent; the
efficiency penalty is like to be higher.
So, once the flow actually becomes turbulent
as we have seen, the flow becomes
turbulent somewhere on the blade surface.
As the local Reynolds number goes up and
typically the Reynolds number above 2 tends
to have 2 to the power 2 into 10 to the
power 6. It typically has a tendency to become
turbulent flow and then of course, you
know it has a turbulent flow characteristic
and necessarily the loss is going to be higher.
So, turbulent flow has a higher loss characteristic
which is frictional loss is basically
what normally you gain in terms of weight
loss. Then of course, the 3 percent turbulent
which is after the natural transition and
then this is what happens if you have a 3
percent
turbulent which is force transition by some
method of tripping, the transition has been
forced and as a result of which you can see
the losses can be reduced.
So, if you have a tripped flow by some means
you can reduce the losses and as a result
of
which you can have lower losses. Whereas,
if the flow is turbulent right in the beginning,
the losses are going to be very high. Now,
in axial gas turbines, in turbines quite often
the turbulence level is quite high. It is
quite often seen that the turbulence levels
are
indeed of the order of 3 percent or even higher.
This is the loss coefficient in terms of a
certain correlation created by a gentleman
called
Soderberg. This gives the loss coefficient
with the deflection of the flow. As you can
well imagine, as the deflection of the flow
that is beta 1 plus beta 2 or alpha 1 plus
alpha
2 increases at a certain point of time, the
loss would indeed start increasing. These
are
given in terms of t by c of the blade 15 percent,
20 percent and 30 percent. As you can
see, the initial losses were very high, but,
you can have losses that are little lower
if you
have control over the blade profile.
So, losses typically would go up if the deflection
attempted is very high. You have to
decide what kind of deflection would be appropriate
for your design. Knowing that at
some point of time you would have to pay a
bit of loss penalty.
Then of course, we come to a very important
issue called blade loading. This is to be
factored in with blade spacing. This is typically
decided because as I mentioned earlier,
if you pack the blades more you get a better
guidance of the flow through the curvilinear
passage. But, your friction losses are high.
As a result friction loss is a primary loss
and
as a result your efficiency penalty would
go up.
On the other hand, if you pack the blades
space the blade apart your guidance would
be a
little less, but, your losses would be going
down and your efficiency would be higher.
So, Zweifel decided way back in 1945 that
value of .8 is a reasonable compromise
between guidance of the flow and the penalty
that you pay in friction loss.
As a result of which, Zweifel criteria have
been used in turbine design for many years.
In
terms of blade tangential loading can be written
down in terms of Z W which is a
Zweifel parameter as in terms of twice by
s by c spacing by chord into cos per alpha
2
into tan alpha 1 plus tan alpha 2.
Now, this allows you to select the value of
spacing. So, one can find out or calculate
the
spacing from the Zweifel criterion and then
decide the number of blades that you should
have. However later, designers have explored
more and have found that this Zweifel
criteria is very good if your exit flow angle
is between 60 and 70 which indeed is
actually a very popular exit angle design
zone.
However, if your exit angle is less than 60
or more than 70 by design, you probably need
to think a little before you apply this Zweifel
criterion because this Zweifel criterion may
not be valid.
So, Zweifel criterion is indeed valid for
alpha 2 between 60 and 70 which is the more
popular alpha 2 design zone. But, if by chance
it is beyond this range, then Zweifel
criterion remember may not be valid. So, you
may not use the value .8 you may like to
use some other value to decided separately.
HTP turbine and LPT turbines the difference
between the two needs to be very quickly
pointed out. HTP blades are short and they
run at high rpms. LPT blades are long. As
you can see, they are 3 4 times longer than
HPT blades. On the other hand, they will run
at low rpms. HPT blades face very high temperature
coming from the combustion
chamber. LPT blades work with very high flow
velocities because through the HPTs the
flow velocity has gone up.
So, the average flow velocity here is likely
to be of a higher order. Because of these
differences the airfoils used for HPT and
LPT are quite different from each other. As
we
have seen very early on they had decided that
t 6 profile is good for hpts and T 1 0 6 is
most likely to be used for LPTs. So, but,
the modern designers of course, have different
approach. They do not use those profiles very
strictly any more.
So, the modern design starts off with an aerofoil
shape T 6 or T 1 0 6 and then it is
modified by CFD certain interactive or direct
method of numerical analysis. So that
means, you feed this airfoil try to find out
its aerodynamic performance and then see
whether it is good for you or you change the
profile again and feed it into the analysis
which is what most people do. However, there
is a indirect method which is normally
adopted towards the end of the design. When
you have a reasonable idea of what would
be the cp distribution over the blade by the
earlier method off iterative or interactive
method and then you feed that final wanted
or desired cp distribution and adopt an
indirect method of creating your blade profile.
In which case, the blade loading is already
decided upon and then you get the final profile
decided upon from the indirect method of
CFD analysis.
Here we see finally, look at supersonic turbine
blade profile. Now supersonic blades are
as you can see they are sharp because they
have to negotiate flow that is coming in with
supersonic Mach number.
So, the blades would have to have sharp leading
edges. There is no scope for rounded
leading edges here which means you cannot
have cooling in these blades. So, typically
supersonic blades like these would have supersonic
flow through the entire blade
passage. It is coming in supersonically and
going out supersonically. Inside of the
passage it would have continuous strain of
shocks or fans.
It is most likely that the flow would be going
through the entire blade supersonically.
One of the oldest methods of designing supersonic
turbine blades is not to have any
acceleration or deceleration inside the passage,
but, a constant supersonic Mach number
blade. That was the earliest design that people
have used for supersonic turbines.
The supersonic turbine blades also are configured
using the method just was discussed in
the last slide. So, there is a certain amount
of difference between what you can have and
then if you accommodate the boundary layer
and the losses that can occur. So, very
slight difference in the flow profiling may
need to be done with the help of modern CFD
methods to get your final blade profile. It
would still have a sharp leading edge and
a
sharp trailing edge. Typically such blades
have been used in rocket motors. Those blades
would indeed have very high temperatures,
but, they are likely to be made of ceramics
or
refractory materials that do not need cooling.
As a result of which you can do without the
cooling methodology. You can simply make the
blades out of very tough material like
ceramics which can withstand very high temperature
and for a certain period of time
specially used in rockets or missiles which
may need to be used for only few hours. Then
they are appropriate and then of course, as
we know, if you deploy supersonic airfoils
in
supersonic turbines, the amount of work done
would be hugely more. You can get very
large pressure ratio across such supersonic
turbines.
So, supersonic turbines are very special things
normally not used in commercial gas
turbines either line based or aero engines.
They are used in very special cases as I
mentioned one of the possibilities is in rockets
or missiles where you have small turbine
machines for turbo pumps.
So, that brings us to the end of fundamental
profile discussion on various kinds of profile
that are used in axial flow turbines. In the
next class, we will be discussing how to use
these profiles and what is the method by which
you finally create a three dimensional
blade from root to the tip of a blade. 3D
turbine blade design is what we will be doing
in
the next lecture.
