We are talking about three-dimensional flows.
Three-dimensional flows in axial
flow compressors, that is what we started
talking about in the last class; and we
solved some very simple examples, through
our some very simple mathematical
derivation; we arrived at a simple law, which
is known as Free Vortex Law,
which again comes out of a very simple radial
equilibrium of forces, also simply
called radial equilibrium condition or sometimes
simple radial equilibrium
equation.
Now, based on those laws, we will today discuss
little more in detail various
aspects of design laws of axial flow compressor
blades.
Now, those are derived
from those Free Vortex Condition that we set
forth in the last class.
However, we
will be moving forward from there; we will
also see, what are the restrictions or
you know conditions based on which Free Vortex
was derived, and those
restrictions would need to be overcome or
you know got around in the modern
axial flow compressor design.
So, we will try to look at, what the modern
axial flow compressor designers are
doing; we will of course, have a more detail
discussion on blade design later on
in this lecture series.
We will have a full lecture on blade design
principles, and
blade design methodology later on.
But today we will just set forth certain
fundamental design principles, design laws
starting with the Free Vortex Law,
and try to put together a certain conditions,
certain parameters and of course, a
certain laws that the designers even today,
start off with for designing a
completely new axial flow compressor blades.
So, starting a completely new axial flow compressor
blade, needs to be started in
very simple way.
We will…
As, I said we will later on look at in more
a
comprehensive method; in which, how the modern
compressors are designed, and
in which we also used various modern saved
techniques; and those things we will
look at a little more comprehensively later
on.
Let us, take a look at what the
design laws - the fundamental design laws,
tell us.
So, today’s lecture is on threedimensional
fundamental design laws for axial flow compressor.
Now, this design laws of course, start off
with the Free Vortex Law, which we
set forth in the last class; we will look
at this be Vortex Law, a little more in
detail; and then we will see that it has number
of restrictions, because it was set
forth or derived based on certain simplifications.
And we will have to see, how
these simplifications can be got around, for
more modern or other more
specifically; more highly loaded, axial flow
compressor blades.
So, let us start off
with what we ended with in the last class
- that is the Free Vortex Law.
Now you see, Free Vortex Law is based on what
we had put together as radial
equilibrium condition, and which had some
simplifying flow conditions; these
simplifying flow conditions, where that in
the radial direction, total enthalpy H
actual velocity, inlet velocity C a and a
density are constant.
Now, these are some
of the simplifying condition that we had used
along with the fact that the flow is
isentropic; and as a result of, which using
those additional thermodynamic
conditions; we had found C w into r equal
to constant.
And this is the Free Vortex
Design Law, which people have been using,
for you know almost 60 years, ever
since, axial flow compressors made their mark
in jet engines.
Now, this Free Vortex Law of course, means
that C w into r means, as the flow
goes from root section of the blade to the
tip of the blade r is increasing; r is of
course, the minimum at the root, and then
it keeps on increasing right till the tip
of the blade.
Now, which essentially means that correspondingly
C w would keep
on decreasing; so, C w is maximum at the root
and minimum at the tip, so that the
product of the two C w and r is held constant,
as per this Free Vortex Law.
So, if
we are using Free Vortex Law, as a guiding
principle of the design, that blade is
likely to produce flow, which would have that
kind of a flow configuration in
which C w, that is the whirl component of
the flow would be decreasing from
root to tip, proportional to the increase
of the radius.
Now, you see when the flow comes into the
blade C w is actually constant; that is
C w 1 coming into the blade is constant.
So, which means it acquires a different
kinds of us C w characteristics, will characteristic
as it goes to the blade.
So, by
the time it comes out at the rear of the rotor,
because of the rotation and because
of the free vortex design that has been used
to create that rotor, that rotor based
on free vortex design would create C w variation,
proportional directly
proportional to r in the radial direction.
So, that the product of C w and r is held
constant.
So, if you create a blade based
on Free Vortex Design Law, you would get a
flow in which C w varies inversely
proportional to r with reference to change
of radius.
Now this is what happens,
when you have a so called Free Vortex Design.
Now, let us see, what are the
ramifications of this Free Vortex Design?
What happens is that the radial equilibrium,
which is used to explain some of the
basic characteristics; the radial equilibrium
requires that in a medium, which is
define as less than 1 radius ratio, and low
that is a much less than 1 hub to tip
radius ratio in a rotor blade.
The change of whirl component must be very
large
near the hub, compared to that near the casing;
if you are blade is such that hub
and tip are substantially separated from each
other, because it has let us say low
hub to tip ratio hub is small, and tip is
far away and the different in r between the
two is quite large; it essentially means that
C w at hub is going to be very large,
compare to that at the casing.
That is what the Free Vortex Law, then tells
us...
So, C w are whirl component at the casing
is indeed going to be very large.
Now, what does that mean; The C w…
The Free Vortex also means that it has a
radial equilibrium.
So that, the flow turning at the hub, must
be much larger than
at the tip.
So, which means, which is a corollary from
which we can draw
corollary, that the hub airfoil must be of
a high camber than that of a tip airfoil.
So, the tip airfoil is likely to be a flatter
airfoil, low camber airfoil, and the hub
airfoil would be a high camber airfoil.
So, as you can see the camber would
indeed vary from hub to tip, which mean you
the essentially have different
airfoils at the hub, and at various sections
all the way up to the tip.
So, they are indeed, different airfoils not
same airfoils.
And then, thirdly the whirl
component downstream of the rotor would be
higher than the upstream.
Now, the
whirl component change of whirl component
of course, is the work done.
So,
since work is been done, work is been put
in, its stands to decent that the
downstream C w or whirl component will be
higher than the upstream one.
Now,
we have already seen that the whirl component
varies along the radius, and that
variations is at the downstream one, because
upstream one depend on what the
flow is coming in and in the first stage for
example, it is likely to be constant
from hub to tip.
So, the inlet whirl component is depended
on how the flow is coming in, what
kind of flow pattern or flow profile is coming
in, the exit profile is decided by the
blade design law.
So, if you have a Free Vortex Law, on which
the blade has been design; the C w
at the rear of the rotor blade.
Firstly, it would be higher than the than
at the front,
that is at upstream one, because the work
has been done.
So, C w at the rear has
to be higher than the C w one at the front;
and then of course, C w varies from
hub to the tip of the blade, as for the Free
Vortex Law.
So, these are the two
things; that happens to the whirl component
of the flow, as the flow goes to the
blades.
So, let is looks at what the other things
are happening what does that
means, if you have C w variation along the
length of the blade.
If you look at this picture, this is the picture
we have used in the last class, and it
tells you that, there is a balance of force,
which is the balance of the static force P
to P plus dp, which was balanced by the radial
force created by the dynamics of
the flow; and one of the major dynamics is
the C w component, which is the
whirl component with which the fluid particle
is rotating with the blades.
And now, we see that somewhere in the blade
C w is higher; somewhere in the
blade C w is lower, which means wherever C
w is indeed higher; it stands to
reason that corresponding change of pressure
would also be higher.
So, that is
what is said said down here, that the radial
static pressure gradient dp, dr will be
greater downstream of the rotor than upstream
one.
So, as the rotor imparts energy into the fluid,
the fluid coming out of the rotor, as
it comes through the rotor blade passage C
w would be higher, and in which case
that value of C w would need a greater dp,
dr or pressure gradient in the radial
direction.
We have also seen that the C w varies along
the ring, length of the
blades; so wherever C w is higher, it would
correspondingly try to give stronger
dp, dr gradient.
The static pressurize across the blade root
will be lesser than across the rotor tip,
this is also comes out of the Free Vortex
Law.
The work done at the tip is likely
to be of higher older than at the where the
u is much higher; and at the blade root
and the value of u is much lower; and as a
result the static pressurize would be
much lesser at the root than at the tip.
And then we come to the more important,
very important parameter degree of reaction,
which we have talk about before.
And the degree of the reaction across the
root will be much less compared to that
at the tip; that is for Free Vortex Blade
Design.
So, degree of reaction need the root is indeed
going to be much lower; in fact,
this is something which we will again come
back later on when we discussed
design; and we have we have already talked
about a little, the fact that degree of
reaction need the root can go indeed so low,
to the extent that it can it can
actually, tend to go below 0.
That means it could tend to become negative.
Now,
negative degree of reaction is not a good
idea, because it indicates at the flow at
that station, at that radial position is indeed
behaving like a turbine and not
behaving like a compressor.
So, in a compressor a negative degree of reaction
indicates the flow is, flow and the rotor
together is behaving like a turbine in that
particular location.
So, negative of degree of reaction is to be
avoided, but all costs if it has to work
like a compressor.
So, it has to be made 0; more than 0, minimum
is 0; and it
needs to be made a little more than 0 if possible.
So, that near the hub under all
operating conditions of the compressor, it
never goes below 0.
So, degree of
reaction is another parameter, which we shall
be discussing in this lecture today,
and we shall see more and more; how it impacts
on the design?
In addition to the
Vortex Laws a starting with the Free Vortex
Law, which we were discussing
right now.
So, degree of reaction is other important
parameter which will be
discussing a little more in today lecture
only.
Now, if you take typical blade profile or
stage design which uses 50 percent
reaction - degree of reaction stage.
What we see is the rotor and the stator are
angled equally; that means, the flow coming
into the rotor at an angle beta, and
the flow coming into the stator at another
angle alpha alpha two is a likely to be
same.
So, these two angles are same.
So, the two blades the rotor and the stator
are set at same angles.
Now, this is of course, to make sure that
the flow coming to in to the rotor in
relative frame, as the same angle as the flow
going in to the stator in absolute
frame.
Now, this has been done during the earlier
lectures.
So, 50 percent degree
of reaction stage blading, which gives as
as we call it a symmetrical blading is a
very preferred, and very popular design choice;
for axial flow compressor design.
The next preferred choice is a high reaction
blading, which could be prediculous
to a 100 percent reaction blading, which has
been a preferred choice of designers
in some parts of the world notably in Germany,
where people have been
designing 100 percent reaction blades for
many many years.
In fact, right from
the beginning some people preferred to design
blades with 100 percent reaction.
Now, 100 percent reaction blade of course,
gives completely different blade
orientation and blade stagger.
So, that what you shown in this diagram for
example, that the blades in the rotor
are now highly staggered at a very high angle
beta, compared to Let us, say 50
percent one, where the angle was moderate
and this high angle comes out of the
high reaction necessary; that means, the flow
in the rotor would has would have
to go through a high amount of diffusion and
the flow in the stator, as we can see
here, essentially is doing a turning job.
It is not doing any diffusion at all.
So,
diffusion in the stator is 0; all the diffusion
is occurring in the rotor, if it is 100
percent reaction.
So, and stator is just a turning wings; a
set of turning wings.
So, high reaction
stage blading is another choice, and many
years it was the 100 percent reaction
blading, which many people have been using;
and that is their design choice in a
division two.
Let us, say Free Vortex.
Now, they the Free Vortex and the reaction
choice are not in conflict with each other;
essentially they are complimenting
each other.
Free Vortex we have seen of course, that the
reaction indeed varies from root to
tip.
So, what we are talking about is a value of
reaction, somewhere in the middle
of the blade or in the mid section of the
blade, mid radius of the blade, where it
could be let says 50 percent.
On the other hand, some people have used a
constant
reaction blading, where the reaction is held
constant.
Now, that kind of blading is
not free vortex design.
So, Free Vortex Design will have reaction
degree of
reaction, varying from hub to the tip.
In which case, when we say 50 percent
blading, the mid radius of that blade has
the 50 percent reaction; someone near
the hub, it is very low that is a 0.5 at mid
radius, at the hub it could be a nearly 0;
may be less than 0.1; and near the tips it
could be of the order of 0.8 or 0.9 which
means 80 to 90 percent reaction blading.
That means, near the tips the blade
arrangement could be very similar to what
we are looking at here, that this is an
arrangement, which you could be seen near
the tips.
Whereas, this is an arrangement you could
be seen near the mid section of the
blade; and near the hub it could be nearly
0, so blades should be the rotor blades
should be even more straightened out.
So, from hub to tip the blades setting of
the
blade orientation would also change, because
the reaction value is changing
based on Free Vortex Design principle.
So, this is the kind of blading, you would
most likely to see in the other tip of the
blade.
So, these are the Free Vortex
Design possibilities.
Now, if you look at some of the other summary
common
that we would like to make.
A stage consists of a rotor and a stator,
if you have a radial equilibrium of forces
balance in the rotor, it would impact the
flow across the stator.
Now, the stator
blade, the rotor blade rows by virtue of the
fact that they working, increase the
whirl component the stator blade rows, would
reduce the whirl component across
its own row; across the entire length that
is from a root to the tip of the blade;
downstream of the stator the radial pressure
gradient dp dr will be much lower
than the upstream of the stator, we had seen
exactly opposite happens in case of
rotor.
The static pressure rise delta p across the
stator, at the hub would be much higher
than at the tip, in the rotor we had just
seen it was exactly opposite; at the hub it
was much less than at the tip, at the state
across the stator it will be a high at the
hub, and low at the tip.
Now, this may lead to high blade loading near
the hub
sections, and even flow separation now increased
blade loading, increase static
pressure ratio; essentially means that the
blade is aero dynamically loaded more.
You are trying to get more out of it aero
dynamically, and that is blade loading.
Now, if you are trying to achieve higher static
pressure gradient, remember this is
in adverse pressure gradient.
So, pressure is increasing from front to the
rear of the blade; and this creates a
situation that the flow gets loaded, the blade
is loaded and the flow is now on the
brink of separation.
This is the problem; that if you increased
the loading at
anywhere, any section of the blade, whether
it is the root, or the tip or the mean
or any others section, if the blade gets aero
dynamically loaded more than what it
can withstand, the flow would indeed be on
the brink of the separation, if it does
separate the blade will get into stall.
And this of course, could blow up into much
bigger problem which we call surge.
So, these are the issues, which the blade
designer would have to factor in, and
they have, he has to take them into a count
that under no operating condition of
this axial flow compressor at any point, at
any section of the blade, would ever be
threading to the under stall or separation.
That means, no where the blade loading
should be more than what it can withstand;
earlier, we had said forth parameters
like diffusion factor as one of the blade
loading parameters.
So, we have to
confirm to those limitations, to ensure during
the design process that had no point
of time, the blade is threatened with separation
and stall, which as I said could
lead to surge.
So, some of these issues would need to be
contented with and as we seen now,
the variation across the rotor is quiet often
different; and is quiet often opposite to
that of the nature of variation across the
stator.
Now, rotor and stator put together
they complement each other; and they put together
make up the whole stage.
So,
what happens in the rotor, and what happens
in the stator are quiet often; opposite
to each other.
And as, I just mention, it is also decided
by the degree of reaction, if it is a 50
percent; the loading is 50 50 across the rotor
and the stator; which normally
happens at the mid radius of the blade or
or mean passage of the blade from root
to tip; and that is often equally shared between
the rotor and the stator.
Anywhere
else, in the blade from the root to the tip,
the share is unequal.
Sometimes the
rotor is loaded more, sometimes the stator
is loaded more, aero dynamically; and
this loading often carries an impending threat
of separation and stall.
So, the
designer would need to keep all this in mind,
while designing the blade.
So, this
is what setting for the basic design principles
actually mean.
Let us, move forward and see what happens,
if you carry on with this design
principles.
The design principles that we have said forward
C w into r.
As, we see
as a number of simplification and number of
constrains.
We just put together, all
those constrains; it loads the blades differentially,
and it loads the blade in a
certain standard, one may says straitjacketed
manner; if you do not like that strait
jackets and most modern designers, do not
like such straitjackets; they would like
to break free from the Free Vortex Design
Law.
And based on this consideration, a generalized
Vortex Law has been put together,
which reads C w into r to the power n is equal
to constant; where, n equal to 1
gives us back the free vortex law.
So, Free Vortex then becomes a one singularity
case out of this generalized a vortex law.
Now, this vortex law has been not been
derived separately, it is simply up gradation
of the free vortex law by using a
value of n; which is sometimes could be other
than 1.
Now, normally the value of n could be from
minus 1 to 2, those other values
people have used in the design.
And, I have found their utility values; and
we will
see; what those values actually mean one of
course, n equal to 1 means, we go
back to free vortex, which we were discussing
discussing in some detail.
Now, let is move forward and see, if the value
of n is something other than 1.
For
example, it is possible that the value of
n could be a little less than 1, and if it
is
somewhere between 0.75 and 1; this yields,
what is often referred to as near-free
vortex or simply relaxed-free-vortex design
in which the blades sections are
slightly over loaded with respect to the free
vortex blade loading.
Now, free vortex blade loading for wide set
an amount of blade loading,
characteristics to the rotor and the stator
blades; this relax free vortex where, n is
less than 1, overloads the blades slightly,
very slightly.
So, that it is not
threatened with separation or stall within
the limits of the diffusion factor which
we have discussed earlier.
And this slide over loading than allows the
designer to have or create more
pressure ratio across one single stage; that
is of course the aim, that you try to
create higher and higher pressure ratio across
one single stage, and in a multi
stage configuration; if you have higher pressure
ratio - pressure ratio across each
stage, you would indeed have less number of
stages.
So, that the overall
intension.
Now, in the process of this you relax the
Free Vortex Law; so, that each stage is
now, slightly more loaded than the Free Vortex
Design, and hence, it is doing a
little more of pressurizing; and little more
pressure ratio across one single stage
design.
So, this is one way of slightly over loading
the blades.
On the other hand,
if you have blades in which the value of n
is more than 1 which is one of the
possibilities, the blades are under loaded
with respect to the Free Vortex Design
Law.
So, moment the values of n used a more than
1, the blades are under loaded.
Now, this is not entirely you know useless;
you may like to under load the blades
under certain operating conditions; and the
reason is near the tip of the blade or
near the hub of the blade, quite often the
blades have to content with the case in
boundary layer; and the hub boundary layer.
Now, these two boundary layers
interfere with the airfoil operation.
And hence, the airfoil do not really operate
like airfoils, as they should near the tips;
and near the hub of the blades.
As a result of which you never get the full
loading anyway, because of this three dimensional
flow nature especially near the hub and the
tip.
In which case, the
blades are not going to give the same blade
loading, same pressurization, near the
tip and the hub; and as a result of which
many designers now feel over the years,
that there is no point loading the blades
so much, near the tip and the hub; might
as well under load them with respect to the
free vortex loading, we are talking
about, and may be the rest of the blade in
between sections of the blade may be
overloaded by using value of n less than 1.
So, that is one way of getting away from free
vortex, the middle part of the blade
is loaded more than the free vortex, the tip
and the hub portions are under loaded
by using a value of n more than 1.
And, this combination is now not a free vortex
design really, it is been relax; and this
new blade now has a better characteristic;
the tips are under loaded, and as a result
it is expected that the tip flow would be
less strong, because the strength of tip flow
is dependent on the blade loading at
the tip.
If you are under loading, the flow across
the tip would be of a lower
strength, and and the tip will be less, the
tip flow vortex will be lower strength,
and hence the blade will hopefully be of a
higher efficiency and hopefully of a
better stall characteristics.
So, these are the thoughts that are put together;
in
using values of n less than 1 and more than
1.
Now, the other possibility is where, n could
be minus 1; which has been use
sometime, it is often called the force vortex
design.
The other possibility is where
n is equal to 0, which is known as Exponential
design law.
If you use n equal to
0, you the see that C w is kind of constant;
the relationship is C w into r to the
power n; when n goes to 0, essentially C w
is constant; and this is often referred
to as Exponential design law.
And this is often used to arrive at or it
is a
derivative of C w is equal to constant.
It gives what is often, then can be called
constant degree of reaction blade designs,
which been the degree of reaction is
now constant from root to the tip of the blade,
tip of the stage.
Now, we have seen free vortex.
And indeed its variants; the relax free vortex
where n is slightly more or less than 1.
The degree of reaction would vary from
root to the tip of the blade.
When using n equal to 0; the exponential law
C w is
constant, and hence the degree of reaction
would be constant from root to the tip
of blade, you can choose a degree of reaction
now.
And the early designers often
used to choose, if they used a constant reaction
blading design; either 50 percent
or 100 percent, nothing in between for a long
time people were using 50 percent
reaction blading or 100 percent reaction blading,
all the way from root to the tip
of the blade.
However, model designers may like to do differently,
and has we shall...
We shall
see as we go long; that the variation of degree
of reaction is indeed an important
issue, and modern designers do have relaxations
of those things also along with
the relaxation of free vortex law.
So, both the free vortex law, and the degree
of
reaction variation is now relaxed.
And it is done in a more control manner, and
hence modern designers would like to call
call that a control vortex law.
So, that
all the design is now under control; the variation
of degree of reaction; and the
variation of the vortex strength from root
to the tip is done in a control manner,
and modern designers would like to call that
a control vortex designs.
So, we have seen that a number of possibilities
do are there, in which you can
actually, create the fundamental blade design
- we are talking about fundamental
blade design; the first cut blade design,
when you are just creating a new blade,
where they was nothing, and you are creating
a new blade.
Let us, move forward
and then let us see what happens, if you use
this kind of blade design laws or
principles.
We have seen earlier that the blades have
vertices created around, because they
are made of airfoil sections; and those vertices
have circulation, and the strength
of circulation or variation of the strength
of the circulation is one of the issues
along length of the blade, which now we see
depends on the reaction or degree of
reaction.
If we have a Constant Reaction Blading, we
shall see that the Vortex along the
length of the blade would remain constant;
and would would vary in a constant
manner across the from one side to the other
at the trailing edge.
We are looking
at it from the trailing edge.
So, it will move from one side to the other
side at the
trailing edge, and you will have a more or
less constant strength, along the length
of the blade that is from hub to the tip.
On the other hand, if you have a Free Vortex,
which is a Variable Reaction
Blading.
And depending on the reaction variation, depending
on the Free Vortex
Design Law that has been used; the strength
of vortex would now be varying
along the length, and this variation is from
here in the diagram.
Now, what happens in a Free Vortex or in an
Relax Free Vortex or the modern
version of control Free Free Vortex Design;
is that it gives a Variable Reaction
Blading or Variable Degree of Reaction Blading.
And as a result of which one
can say that the nature of the vortex formation,
and the strength of vortices from
hub to the tip depends on the blade design
laws, and the blade geometry and
indeed the operating condition.
So, what happens is that the vortex formation
from hub to the tip of the blade
depends on design laws, that we are discussing;
it depends on the blade geometry,
and very importantly it depends on the operating
condition.
You see we have
talked about before the blade is designed
at a particular operating point, which is
known as a design point.
But the engine and the blades, the compressors
would
have to operate under various operating conditions,
where the speed of rotation
rpm, the mass flows or different from the
design point.
So, the design operating point, if it is away
from the design point would indeed
impact on the vortex formation.
The vortex formation depends on three things
design laws, blade geometry, and the operating
condition; at which the blade is
operating.
Now, the preliminary designs, also driven
by what we have discussed as the
degree of reaction, along the blade length.
Now, the three limiting possibilities
are often started with, when you are creating
a first cut blade design; the three
possibilities are - degree of reaction equal
to 0 percent, degree of reaction equal
to 50 percent that is the most popular one,
and degree of reaction100 percent.
Now, we look at these three possibilities:
The 50 percent reaction blade
essentially creates equal diffusion diffusion
in the rotor and in the stator; that in
the blade loading or equal between in the
rotor and in the stator.
And the
diffusion is equally shared.
Now, the three limits that we are talking
about 0 to 100 percent in a free vortex
design.
It is entirely possible that from the root
to the tip of the blade, the degree
of reaction would be varying from 0 to nearly
100; that means, different sections
of the blade have different reactions.
So, at the hub or near the root; it could
be
nearly 0, at the tip it could be nearly 100;
someone in the middle its 50 percent.
Now, that is a kind of variation, that is
quite often people have used in the blade
design; the other possibility which we talked
about is that Constant Reaction
Blading, where the entire blade has constant
reaction; and in which case also
three are possibilities - 0 percent, 50 percent,
and 100 percent.
Let us see, what that means actually?
When you have a 50 percent Reaction
Blading, the blades are equally loaded.
When they are other than 50 percent, you
have to remember that either the rotor or
the stator is going to be more loaded.
Now, the two limiting cases we discussed are
0 percent, and 100 percent
reactions played between the rotor and the
stator.
And this reaction, now varies in
free vortex or near free vortex would vary
substantially from root to the tip of the
blade, which means from the root to the tip
of a stage, the split between the rotor
and the stator would vary from the root to
the tip of the blade; that means, the
loading pattern would vary from the root to
the tip of the blade of a rotor, and the
loading pattern on the stator would vary in
the opposite manner from the root to
the tip of the blade.
Now, this is what exactly a free vortex or
a near free vortex design would
essentially yield.
So, this variation from the tip root to the
tip of free vortex kind
of design is an important issue; we have to
keep that in mind unless you are going
for a Constant Reaction Blading.
If you have a reaction that is 0 percent,
a limit; the entire diffusion happens in the
stator.
And that means, the rotor is not having any
diffusion at all, hence the rotor
is been used only for imparting work into
the flow, energizing the flow, putting
work into the passing flow; and such a rotor
will not have any diffusion by design
occurring in the rotor blade passage.
Hence, such a blade may be called impulse
rotor, very similar to the impulse turbine
that you may have heard of.
We shall
we doing it in the turbine chapter later on,
and hence the energy transfer happens
due to the turning of the flow.
So, the turning of the flow essentially, is
equated or responsible for the amount of
energy transfer; and no diffusion is occurring
in that particular rotor in which
degree of reaction is 0 set forth as 0.
Now, many supersonic rotors may have a
degree of reaction, 0 percent.
It is possible, that subsonic rotors may also
have
one of the possibilities is the supersonic
rotor, where the flow is supersonic
through the rotor blades, and during that
lot of work transfer is accomplished.
However, the diffusion is differed to the
stator; mainly, because the rotor is busy
transferring energy into the fluid.
In case of a 100 percent blade design; it
is
exactly opposite.
Rotor is now doing energy transfer, and energy
conversion; 100
percent into pressure.
So, energization and then pressurization 100
percentage
occurring in the rotor, nothing is left for
the stator.
What is the job of the stator?
Stator essentially, turns the flow.
Because in that kind of a design, it is most
probable the stator will have a lot of turning
to do; and as we have seen before,
doing a lot of diffusion that is a diffusy
passage, and turning the flow around a lot
or two things which are of conflicting interest.
They conflict each other; and a
flow would refuse to do two things simultaneously;
a lot of tuning, a lot of
diffusion.
Sometimes a lot of turning with a small bit
of diffusion may be a
difficult thing.
In which case, the diffusion is completely
dispensed with and the
stator is asked to do only turning; and the
entire diffusion is finished off in the
rotor itself.
So, that is a 100 percent reaction blading.
And as, I mention, there are some
designers, notably got a few from Germany
have preferred that kind of design.
Where 100 percent energization and diffusion
occur in the rotor and stator
essentially, turns the flow for the next row
of blades or for any other delivery
purpose.
So, these are the limits of various Reaction
Bladings; that we have been
talking about, and as I mentioned the variation
of reaction is as important as the
free vortex law or the vortex law, that we
have brought forward for blade design
purposes.
Now, let us look at some of the other issues,
I mentioned that geometry is an
important parameter.
Let us, look at some of those issues.
Now, if you have a
blade, which is let us say a small size axial
compressor, that will impact that
design or it will tend to take the design
in a different direction compared to a
blade, which is a large size axial fan, as
one can see in a bypass turbo fan.
The
blade design law of such a large sized axial
fan, would be quiet different than that
of a small sized axial compressor.
The first stage of a multi-stage axial flow
compressor, which is likely to be a
comparatively large size blade would be different,
and would probably use
different kind of design law combinations,
compared to that of let us say a middle
stage of a multi-stage or that of a end stage
of a multi-stage compressor.
And then
again all of them put together, we can say
that the particular blade would be
either high hub to tip ratio or low hub to
tip ratio stage.
High hub to tip ratio means that the different
between the rotor and stator is very
small; and the blade is set at a high radius,
which is typical of end stages of a
multistage compressor.
Low hub to tip ratio on the other hand means,
the hub is
low, and the tip is far away and the different
between the two is quite large and
the ratio is small; the systifical of the
first stage of a multi-stage compressor.
As, I
am saying that the design laws that you require
to bring forward, to design these
kind of stages are different from each other;
you may like to use different
combination of design laws, different combination
of reactions or reaction
variation to create these stages.
So, even if you have one single compressor
consisting of multi-stages; each of
those multi-stages of a multi-stage may be
design as per different design laws.
You do not use, same design laws for all the
stages; you use quite often different
design laws for the different stages of a
multi-stage compressor.
The other way of
looking at the stages is, when you have blades
which are often referred to as high
aspect ratio or low aspect radio blades.
Now, if you have a low hub to tip ratio
blade; typically, you would probably looking
at a blade which is something like
this.
Now, this blade you can see is a long blade;
and you can see its quad is very
small, which means its length to quad ratio
is very high, and that is aspect ratio.
So, aspect ratio is nothing but length to
quad ratio, and this is a high aspect ratio
blade; and this one can say also very confidently,
that this is a low hub to tip ratio
blade, rotor blade.
And typically a low hub to tip ratio blade
would tend to have a
high aspect ratio blade, where the quad is
small compared to the length of the
blade.
On the other hand, if you take this blade,
which is again a typical twisted blade,
but as you can see it is a small blade, and
its length is small compared to its quad.
So, this is a low aspect ratio blade, comparatively
low aspect ratio blade; and this
could be used for middle stages of a multi-stage
compressor.
On the other hand, I
will show you another blade, which is let
us say, a low aspect ratio blade.
Now, this you can see the quad of the blade
again a twisted blade, is almost equal
to the length of the blade.
Now, which essentially means that this is
a blade with
aspect ratio close to one; and this is the
kind of blade, you might seen sometimes
in the rear stages of a axial flow compressor,
where the blades are indeed very
small.
We will discuss the effect of aspect ratio
later on, and we shall see that
more and more designers, on moving towards
lower aspect ratio choices in the
modern axial flow compressor design.
Let us, look at a few numbers that you need
to set forth for design of multi-stage
axial flow compressor.
In the initial stages, you would be looking
for efficiencies
which are likely to be a little lower, because
the blades are big and high aspect
ratio; and they often have a certain amount
of distortion or non uniformity at the
inlet.
And hence, quiet often the penalty is paid
in the in form of efficiency; in the
middle stages those problems do not exist.
So, the efficiency is going to be very
high; and in the later stages the blades are
very small, as a result of the smallest
the three-dimensionality of the flow, impacts
on the blade flow; and as a result
efficiency again tips a little, to somewhat
low values.
The pressure ratio of the initial stages,
in spite of low efficiency is likely to be
high, because you are operating at a low pressure,
and low temperature; and due
to the low temperature operation even with
moderate amount of work input, you
can get a very high pressure ratio.
So, while design most designers like to
accumulative very high pressure ratio in the
early stages, because in the later
stages you progressively get less and less
pressure ratio to the extent that in the
last stages, you get very low pressure ratios
anyway; so by design, the designers
like to put more work, now delta T 0 of course,
is a measure of the work input;
and as a result of which they like to put
in more work to get more and more
pressure ratio, which is easier to get at
the initial stages.
Because of the low
temperature operation in a middle stages,
you put middle amount of work and
you get reasonable amount of pressurization;
in the later stages, there is indeed no
point putting very high work input, because
the pressurized is not going to be
very high anyway.
So, that is a kind of first cut division of
labor, who want me
like to do across the stages in a multi-stage
configuration.
Following those configurations, you design
the blades.
So, the design of the blade
would then be dependent on a number of 3-D
flow features; so, these 3-D flow
features are, set forth as you are going to
have a radial variation of Mach number
and Reynolds number.
To the extend, the flow could move from subsonic
near
the root to supersonic near the tip, and the
Reynolds number would also vary, and
hence you would probably need to choose different
kind of airfoils near the root
than compare to that near the tips.
So, you have radial variation of density and
pressure gradient.
Even you are
simple radial equilibrium condition that we
had set forth, the balance of forces
does give you notion that the radial variation
of density, and pressure gradient
would follow the variation of Mach number.
Then consequently, the blade
thickness also would vary from root to the
tip due to the Mach number.
And as, I
was just mentioning that low Mach number near
the root would warrant, low
speed airfoils choices at the tip, high Mach
number would warrant choices of thin
airfoils, which are meant for high Mach number.
If it is supersonic, he would
need to choose supersonic airfoils.
We will discuss those, airfoil issues later
on in this lecture series.
As, we have
seen the work input variation in a free vortex
was considered constant from root
to the tip.
Now, we can see that, one can have a radial
variation of work input
from root to the tip in a control manner;
if you are going for a control vortex
design; that is breaking free from free vortex
design.
This means that the hub and
casing geometry depending on the pressure
ratio.
If you have indeed pressure
ratios of the order of 1.5 or so, your hub
and casing is not going flat any more,
they are going to be at an angle.
And this hub and casing geometry then
introduces a radial flow into the flow going
through the blades.
So, this is introduce by the hub and casing;
angle that is warranted by the high
pressurize.
And then of course, you have the leakage at
the tip of the blade, which
through the axial, and the axial gaps; which
creates the tip vertices; and they
introduce three-dimensionality, you have here
blade due to various operations of
the requirements of the engine or their craft,
and those blades again take away
flow from somewhere in the middle stages;
and they introduces threedimensionality intermediate
stages.
And then of course, all of them put together
you have a secondary flow development; which
is all of them put together.
And also depends as, I mentioned earlier very
strongly, it depends on the
operating point.
So, you may have a low secondary flow at the
design point; at an
half design operating condition, the secondary
flow may be very strong.
Then
again it depends on the non uniformity of
the inlet flow, as we have seen the flow
becomes progressively more and more non uniform.
As it goes through the
stages, then you have combination of subsonic
and supersonic flow; some are
along the blades length you have shocks, some
are you do not have shocks.
So, that produces a three-dimensionality all
over again; and then the radial
variation of all these design parameters is
package together in a high or low hub
tip ratio blade, which as I mention is given
in a high aspect ratio blade, which I
showed you on blade - where the aspect ratio
was close to 6.
So, anything higher
than 2 is normally called higher split ratio.
Whereas, the last blade, which I
showed actually had a aspect ratio close to
1; and that is a low aspect ratio blade.
So, radial variation of parameter is less,
in a low aspect ratio blade, which is
typically high hub to tip ratio blade and
typical of the last stages of a multi-stage
friction of a compressor.
So, we we see that we have number of issues;
we have the vortex law, we have
the variation of degree of reaction, we have
the blade geometry blades are
twisted, and you may like to control the twist
with the control vortex design and
then of course, you have the aspect ratio,
which needs we chosen by the designer.
So, the modern designers are going towards,
somewhat lower aspect ratio
compare to the first blade, which I showed
which is a very old blade.
So, that
kind of blade is not used in the modern blade
designs anymore.
So, those are the
choices, the blade geometry the variation
of degree of reaction; and the vortex
law.
These are things that are put together, which
the designers would like to
create a new blade, package in which new blade
creation can be started.
We shall discuss, more of this compressor
blade design in more detailed, in a
later lecture.
And we will bring all of them together in
a design package in a step
by step design methodology.
In a next lecture, we will look at a full
mathematical form of the threedimensional
flow, which is what we are discussing in this
lecture.
In the last
lecture and in today’s lecture, we will
continue with the three-dimensional flow,
and try to see whether we can have a mathematical
formulation; a more
comprehensive one then the free vortex radial
equilibrium- simple radial
equilibrium equation; that we had done.
A more comprehensive one, that takes
into a count many of the three-dimensionalities
that we have talked about in
today’s lecture; and we shall see whether
we can capture all that, in it
mathematical form that is want we will be
doing in the next lectures.
