We have been talking about axial flow compressors, their fundamental theory. To some extent we
have covered the ground on various aspects of three-dimensional flow through the axial
flow compressors. In today's class we will initiate some discussion on how these axial
flow compressors are indeed, designed. We need to understand, that axial flow compressors
are essentially, uniquely designed. They are not the kind of products, that you can buy
off the shelf or they are not the kind of product you can easily create with the help
of, you know, very simple hand books, design hands books. There are no, you know, design
hand books or designing axial flow compressors and turbines. So, these are aerodynamic machines,
as we have called them, and these aerodynamic machines are typically uniquely designed and
created. So, every axial flow compressor in every aircraft engine is uniquely designed.
There is almost no possibility, that one particular compressor from one engine can be used all
over again in another engine. The possibility is extremely remote and normally it is not
done, which means, that every time a new aircraft engine is created, a new gas turbine engine
is created, the axial flow compressor inside that would need to be designed afresh, in
fact, right from scratch. Now, this requires a lot of effort. In fact,
it takes more time to design that part of the engine than indeed any other part of the
engine. It takes more time to design a multi-stage axial flow compressor than any other component
including commercial chain turbine or other components.
So, it is a costly business, it is a time consuming business, it also requires a team
of people, lot of people to work towards creating this new axial flow compressor unit and it
requires a lot of effort. It is costly because it requires effort in terms of design, it
requires effort in terms of computational analysis and then, it requires a lot of effort
in terms of actual rig testing before it can be considered as a good enough peace of axial
flow compressor for actual engine. So, lot of design analysis and testing is
required before you can say, that a certain design is final and can go on an inside an
engine. There is a lot of matching to be done afterwards when it has to go inside the engine,
but that is a separate issue all together. So, the whole business of creating an axial
flow compressor is a long grown out affair. It takes sometimes years for a team of highly
qualified engineers with PhDs and Masters to create a multistage compressor.
So, some of these things need to be understood, that the do come out of some of the theories,
that we have done and we will try to encapsulate some of the things, that we have done in the
last few classes into a first cut, a very simple methodology with which one can possibly
create an axial flow compressor design. However, that is only the beginning, that is only the
start of a long grown out of work, which would require a lot of people to work in it and
a lot of time and effort to be spent in it, so that you have an axial flow compressor,
that is comparative, that has good performance, good efficiency and matches with the other
components of the engine, that is indeed, very important; you have to match the compressor
with other components of the engine. Now, some of these things we may be talking
about in some of the other lectures, in this lecture series, but today we will be talking
about a method or a methodology by which you can initiate or create a first-cut compressor
design. So, over a period of 2 lectures I will try to bring to you, what fundamental
theories can be used to create an axial flow compressor. So, we start with axial flow compressor
design. Now, when we talk about design you need to
understand, that design is something, which you undertake, essentially to create a product
for a particular performance. Now, this performance is something, which you have to decide a priory.
An engineering product is created to perform. In case of aerodynamic machines, like compressors
and turbine, the performance schedule has to be very accurately pre-decided and design
is accurately made to need that particular performance requirement. If the performance
requirement is not accurately pre-created before the design is undertaken, the design
process would be long grown out before you can finalize the design. So, it is necessary
to create a performance schedule on which the design is to be created.
Now, this performance schedule essentially is another issue, which we will be talking
about a little in today's lecture also, that you need to create, what in aircraft engine
terminology is known as design point. An aircraft engine is designed to perform or give its
performance at its best at its design point. Now, this design point has to be decided a
priory. Is, it is something, lot of thinking, lot of parameters and lot of matching between
aircraft and engine and various components of the engine have to be thought about before
you can fix the so called design point. We shall see later on, that before the design
is finalized, indeed we would need to think about how this particular component or the
whole engine would behave under so called off design operating conditions because a
typical aero-engine operates under many off design operating conditions. And if you do
not take care of them to a large extent during the design process, some of the off design
operating conditions may be very poorly performed, something which an aircraft engineer would
not like to risk any more today. So, those are the issues that would come up before the
design is indeed taken up.
Let us look at what constitutes design. When we talk about design, there are two aspects
that come into the design, one is creating the blade shapes, another is creating the
compressor flow track shape. We will take up the flow track shape first and come to
the blade shape design a little later. Now, we are talking about a multi-stage compressor,
which by now, you know, actually is composed of a number of stages. So, the flow comes
to the initial stages, gets compressed and as a result, you actually require less and
less flow area for the flow to be processed and send backwards inside the engine.
Now, this fundamental aerodynamic requirement born out of continuity equation requires that
your flow track gets narrower and narrower as it goes through the compressors. So, it
enters the flow into the compressor and as it gets compressed, it requires less and less
area, and as a result of which you require much less area over here than at the entry.
And now, these two ends ought to be decided first, what is the pressure ratio across the
entire compressor that comes out of the initial engine analysis, the cycle analysis and the
engine configuration, that has been decided upon and that engine configuration decision
provides the initial compressor ratio. This compression ratio decides prima facie,
what is the pressure ratio across this and hence, what could possibly be the density
ratio across this. That mean pressure ratio and temperature ratio across the compressor
are known and hence, density ratio can be found and that density ratio essentially,
gives us prima facie, what should be the area ratio across this. Of course, assuming or
considering, that mass flow is conserved, whatever mass of flow is coming in here, same
mass would be going out of the compressor. Now, what happens is, this flow track is then
decided by the step by step change in density. Density changes with the pressure and now,
step by step change in density actually provides the flow areas required at various stations
so that the annulus area required at any station is found out from the local density, which
you can find out from the local pressure and temperature values.
Now, to get the local temperature and pressure values, you need to know what is the step
by step pressure ratio that is going through the multi-stage configuration. Now, to do
that, the overall compressor that has come out of the overall engine design, now needs
to be decomposed or split into so many stages. Now, that is one of the things, that needs
to be done and once that is done, you can create the flow track.
We will have a quick look at how to split an overall compressor into number of stages
very shortly. We will quickly take a look at, if we have the number of stages decided
priory, then how do you create the flow track and what kind of choices do you have?
Now, this first flow track, that we are looking at, is a flow track in which the tip diameter
of the compressor is held constant and the hub diameter is allowed to change. As we can
see here, the hub diameter has changed quite drastically in the initial part of the flow
track. Now, this is typically done for high pressure ratio compressors in the initial
stages of a multi-stage. So, all multi-stage compressors have high pressure ratio initial
stages and the pressure ratios are much lower in the later stages. So, the flow track there
is normally in or rather shallow or almost parallel to each other, whereas the flow track
requirement in the initial stages requires a sharp change in area.
Now, this sharp change area has to be smooth and this smooth flow track creation is one
of the first things that a multi-stage compressor designer would need to create after creating
the split in the stages. Now, the first choice, as we see, is where
you keep the tip diameter constant and the hub diameter is made to change to effect the
change of area of the flow. Now, this gives us a situation, where the U tip is maintained
very high through the entire multi-stage configuration. The tip diameter being constant, the value
of the tip blade velocity, U tip is held constant. And this allows the value of the work done
by the various stages to be held more or less constant through the entire multi-stage configuration.
Now, this is something, which people have done over the years because this is one of
the things that allow you to give high U tip value and increasing U mean. Now, as the U
mean is increasing, the mean work done through the stages also amenable to increase. So,
you can increase the mean work done through the stages as you go towards the later stages,
and as we know, in the early stages with modest amount of work input, you get a very high
pressure ratio. In the later stages, even with high work input, your pressure ratio
or pressure rise is going to be rather small. So, we would like to put a good amount of
work through all the stages and increasing U mean is an attractive proposition.
This particular change of flow track allows rapid change of density through the stages
by changing the hub diameter and the tip diameter corresponds to, let us say, a high tip diameter
that is allowed by the engine designer. Compressor designer would have to design his engine within
the overall space allotted to him by the engine designer. And hence, the maximum size that
is allowed by the engine is used for this particular compressor design in which the
tip diameter is held constant.
In the next choice, is exactly opposite where the hub diameter is being held constant and
as a result of which the U mean, now you can see, is continuously decreasing through the
stages. So, stages would have lesser and lesser work input as it goes towards the rear stages.
So, you have high work input in the first stage and then, corresponding lesser and lesser
work input through the rear stages. Now, this is sometimes done quite deliberately
because if you are trying to put in a lot of work through the stages, as we know, the
density changes very fast and the flow track area requirement would also go down very fast,
which would mean, that the size of the blades, that you would need to put in rear stages,
would go down very fast. Now, very small sized blades are not favored
by the designers because they are amenable to aerodynamic flow distortions and loss of
efficiency during actual operation. So, very small size blades are often, not favored design
choice of the compressor designers. To avoid that situation, this is, one of the choices
was, if you keep the hub diameter constant effectively, the compressor overall or mean
diameter is being brought down. As a result of which the density change is much slower
and as a result the size of the blades is, does not go down so fast and hence, reasonable
blade span or blade length is arrived at y design, which is comfortable for the compressor
designer and is not amenable to lot of loss of efficiency under various operating conditions.
So, this is the other choice, which the compressor designer often uses and it is often used in
the middle stages, as I mentioned, to avoid the blades going very small.
The next choice, which is a kind of a very obvious mean choice, in which the mean diameter
of the flow track is held constant, which of course means, that the U mean or the mean
blade velocity of the rotors or various stages is held constant throughout all the stages.
So, the mean work done or the average work done of all the stages, work done per unit
mass flow, of all the stages is actually held constant.
Now, this is, as I mentioned, a very simple and obvious choice of most designers and gives
rise to a compressor, in which both the tip diameter and the hub diameter would have to
be changed simultaneously. Now, it is entirely possible, that here, what I have shown is
the hub and tip diameter are changing almost in a similar manner. That means the curvature
of the tip and the curvature of the hub, that is shown here, are exactly mirror images of
each other. On the other hand, it is entirely possible, that the modern designers would
make a little diversion here and make a choice in which the curvature of the hub and the
curvature created at the tip for the flow track are not exactly mirror image, they are
different. And as a result, it is possible, that the mean diameter or the mean, U mean,
the mean blade velocity would vary slightly through the stages and this is done deliberately
by the modern designers to exert a little control over the change of density, that occur
through the stages, which as I mentioned, allows them to control the size of the blades.
The combination is, of course the choice of the modern designers, where in the initial
stages you have the hub diameter going down very fast and in the later stages, you have
the tip diameter going down and as a result of which, their later stages, the blades sizes
are not very small. If this had continued to go up like this, the size of the last stage
blades would have been extremely small because they would be operating at very high U mean,
and as a result of which they would require a very small blade size. And the flow track
annulus area would be very small and that would something, which the compressor designer
would not like to favor because two small blades, in terms of blade length, is something,
as I mentioned, quite often creates aerodynamic efficiency penalties.
So, this combination is to avoid the fact, that the blade size towards the end is not
very small, it is little more than very small ones and as a result, you have a control by
creating this combination, you control the size of the blades.
Now, in a multi-stage environment, this combination also allows, that this front part in which
the hub is changing may be one spool of the compressor and the 2nd part could be the 2nd
spool of the compressor and the intervening duct would have this kind of shape. We shall
see later on, that is quite often the done thing that this combination is indeed used
to, for a multi-spool, multi-stage axial flow compressor design.
So, many of these variance of these four shapes, that we have seen, are quite often used in
actual multi-stage compressor design, many of which are indeed multi-spool.
So, these compressor stages, then actually are arrived at, from the mass flow and the
continuity applied, to the local flow through the stages. The split of the stages, we will
be talking about a little later today, allow you to calculate the annulus areas at various
stations and then create the flow track. Now, you see, when you just calculate the
flow areas and put them together one after another, the flow track need not really be
smooth. It is entirely possible, that you arrive at a flow track just putting all the
areas one after another or various stages after the rotor, after the stator and after
the rotor and stator and so on and so forth. You might get a flow track, which is not smooth,
it may be zigzag. Now, that is a flow track that is not expectable; flow track has to
be smooth, it has to have a smooth, aerodynamic flow from the 1st stage to last stage of the
axial flow compressor. So, not only you have to create the work distribution of the stages,
you also have to recreate the work distribution in a manner, that the density variation, that
you get actually, finally, gives you flow track, that is smooth. Until you get a very
smooth flow track, your design is not complete. So, a multi-stage compressor designer finally,
has to create a smooth flow track. In creating very smooth flow track, the fluid
flow equations would have to be used and the compressor work distribution, the pressure
issue distribution, the sizes of the compressors would have to be moderated in a manner, that
finally, you have a smooth flow track in which all the blades are very nicely fitted in a
manner, that, that they actually give very high efficiency performance.
The other business, which quite often is done is, as I was mentioning just a little while
ago, that in multi-stage compressor, you also have multi-spool. You have the high pressure
spool and then, you have the low pressure spool in front of it. In between these two
spools, quite often you have, what is known as an inter-spool duct.
Now, this inter-spool duct, during which there is no compression flow, is going from, high,
low pressure spool to high pressure spool and then, this passage has to be done smoothly.
It also needs to be done in a manner, such that the entry to the high pressure spool,
this is not only smooth, but it provides a uniform flow into the high pressure spool
1st stage. That means, as far as possible, the uniformity of the flow needs to be restored,
which may not be true when it is coming out of the low pressure last stage. The flow may
be, you know, having an old component or a rating component; the pressure distribution
along the length of the blade may not be, you know, uniform. There are many such non-uniformities
with which the flow comes out of the low pressure spool, the intervening duct. Now, the, the
inter-spool duct has a job, as far as possible, to restore uniformity of the flow before feeding
it into the high pressure spool and this is something, which the flow track designer has
to achieve by designing the flow track. So, the flow track design has a number of responsibilities
actually, to discharge in creating a multi-stage, axial flow compressor flow track design.
Many of these modern flow track designs would indeed, not only require design of the various
stages quite often, as I mentioned. You may have to redesign and re redesign those stages
to create a smooth flow track, to fit into a smooth flow track. So, it is an iterative
design process of various stages; till that process is over you do not get into individual
blade design. So, individual blade design of rotor, stators, come only after this multi-stage
configuration has been finalized and completed. Now, to do that, many of the modern designers
also use computational flow dynamics because rig testing is often very costly and that
can happen only after all the stages are designed and fabricated and put on the rig, which is
a very costly affair and time consuming affair. Much before all that, you can have a computational
flow dynamics to aid the process of flow track design, to aid the process of compressor design.
So, quite often, many of the modern designs are indeed aided by computational flow dynamics
or CFD towards creating the final flow track shape.
Now, some of these things are initially created with the help of some very simple considerations.
So, what we are looking at is a simple conical annulus track. So, the track is annulus, if
you remember. However, the construction of the track can be considered to begin with
a conical one. Now, we have seen, this cone can be a curvilinear
cone of various kinds that we have just seen. If we just consider it as a simple conical
flow track, a very simple mathematical expression can be used to capture this conical, linear
conical flow track. Now, what happens is, simple fluid mechanics
or aerodynamics would tell you, that you would like to restrict this angle of this flow track
of angle of this cone to certain values, which could be definitely less than, may be, 10
degrees at any point, at that time, or any, any, any point on the space in that compressor
flow track. Normally, it may be of the order of 6 to 8 degrees, modern designers are trying
to go to higher values. If we go to the earlier flow tracks, that
we had a look at, if you look at this flow track, you would see that in the initial stages
this curvature would seem to be giving you a flow track angle of a much higher order.
However, if you come very close and take a very close look at the change of angle of
the flow track from one point to another, between two very nearby elements, you will
probably find, that the change of angle between, let us say, this point and this point is indeed
actually very small. So, a bit by bit in a curvilinear manner, a lot of change of angle
has been effected in this particular design, but a very small angular change is theoretically
possible through the flow track, if one considers fundamental aerodynamic.
So, this is a very simple, you know, theory, which people often check out to ensure, that
at, at no point of time you are violating the fundamental aerodynamic principles and
the checks and the limitations, that need to be kept in mind while you are designing
this modern axial flow compressors.
If you look at this very modern axial flow compressor design, you would see what I was
talking about. In the initial stages you have a flow track that is very rapidly changing
through the stages; you have a rotor, stator, rotor, stator, rotor, stator. So, it is a
3 stage low spool, low pressure, high compressor spool, which allows the flow to flow into
the high, high pressure spool, which comes later on, which is a 6 stage high pressure
compressor. And as we can see, the flow track here has
rapidly changed because of large amount of work that has been pumped into the flow and
rapid change in density. And then, the flow is compressed and it is again ducked into
the high pressure spool. As I was mentioning quite often, the high pressure spool is at
a lower average radius than the average radius or diameter of the high pressure spool.
So, the U mean in the high pressure spool is much lower than the U mean of the low pressure
spool and of course, the U tip of the low pressure spool, to begin with, is very high.
The U tip here is continuously, go down, going down, as we can see.
Now, high pressure spool, here is, where both the tip and the hub diameters are changing
almost linearly towards the end of the high pressure spool. Whereas, here, they are changing
in a curvilinear manner and the change at the hub end is much faster and the change
at the tip end is much shallower, but it is changing at both the casing and at the hub.
And by the time it hits the 3rd stage of the low pressure compressor, the flow needs to
be now ducted inwards into the high pressure spool and hence, the tip actually starts coming
down and the hub also starts coming down. So, the flow track here, first taken a downward
turn because the flow now has to be sent downward into the high pressure spool and of course,
this is a low bypass engine. So, small amount of air would go bypass into the bypass duct.
So, this is a modern axial flow compressor, flow track design, which as you can see has
used the concepts, that we were talking about a little earlier, but used them in a very
clever manner to create a modern two spool, multi-stage compressor configuration.
Now, we come to the fact, that to create a compressor you need to fix the design point.
Now, design point fixation is often done on the basis of a number of parameters. We will
look at the compressor characteristic map, which you have done before in the characteristic
map. If you remember, a functional relationship was established between the performance parameter,
which is the pressure ratio. The efficiency and the temperature change, that occurs through
the compressor, which is a measure of the work done normalized by the entry temperature.
Now, these performance parameters are connected to the, functionally connected to the various
flow parameters, which is the mass flow parameter, which we have said earlier, is a normalized
mass flow parameter, the Reynolds number of the flow and the normalized speed of the rotors,
that are being utilized inside the compressors. So, these parameters on the right hand side
are not really non-dimensional parameters. So, we call them normalized parameters because
actual non-dimensional parameters are not very useful, in the sense, they carry some
parameters, which are dimensionally to be fixed by design and at this stage of design,
they are not yet fixed. So, we consider the parameters, which are not non-dimensional,
but normalized and are useful for characterization of compressors.
So, this is the kind of compressor characteristic, that you have done before and we will take
a quick look at this characteristic map. Now, this line, that you see, is the characteristic
of the compressor at its so called design speed.
Design speed is given by, in by rotor over T 01 and this end is the end design. Now,
this has to be decided as quickly as possible, what should be the design speed of the compressor
and then, you quickly arrive at this non-dimensional design speed. Then, the characteristic of
this compressor needs to be decided upon. The first-cut characteristic, that you get,
may not be the final characteristics because that you would get only after the compressor
design has been completed. So, you have a provisional characteristic
map, that may come out of the engine overall design and that give some idea about what
kind of characteristic map the overall compressor should have, so that you can initiate the
design process. At the end of the compressor design, you would create a more detailed characteristic
map out of various theory and CFD, that is available and that could be used as the design
map, till the compressor is tested on the rig. Once the compressor is tested on the
rig, you get the actual design characteristic map of the compressor that has been created.
So, this map design map is provisional one to begin with.
Now, you need to fix the design point. Now, you can see here, there is a problem. The
problem is a typical axial flow compressor, as we have done before, has a peak pressure
ratio, some are over here and immediately flowing the peak pressure ratio. That means,
if you somehow total the mass flow, the mass flow comes down a little, the compressor would
have a tendency to go to stall and it could become uncontrollable stall into search. Now,
that is not an area where your compressor should be working.
On the other hand, if the compressor works at a higher mass flow on the right hand side
of this characteristic map, it would be working at a lower pressure ratio. Now, as far as
the engine is concerned, higher the pressure ratio more is the engine efficiency. The basic
thermodynamic efficiency of the engine is directly related to the compression ratio.
So, higher the pressure ratio, operative pressure ratio, higher is the operative efficiency
of the engine and this is true for all kinds of heat engines. So, you would like to peg
your design point at a higher pressure ratio with the provision that the compressor would
work under higher mass flows, where you would get lower pressure ratios.
If such a working operating point is accepted for a particular engine operation or the engine
aircraft operation, that is fine and you can make the compressor work under such a condition.
Let us say such a condition is 0.5, where you are working at a higher mass flow of the
engine, through the engine, but it is working at a lower pressure ratio. Typically, 0.5
could be representative of the aircraft cruise operation condition. When the aircraft is
cruising at very high altitude, the compressor is often working at a higher throttle, open
higher throttle, at which the non-dimensional mass flow is little on the higher side and
the necessary pressure ratio is on the higher side because at high altitude, you can manage
with low thrust creation. But your design needs to be done for high pressure ratios.
Now, if you peg the design point over here, at a higher pressure ratio, so that it can
produce a little higher pressure ratio if required, which may be required during takeoff
or cline. You cannot work at low pressure ratio during takeoff and cline under those
situations. You have a little problem over here at hand, if the pressure ratio is pushed
to higher values, you can do so only by throttling the mass flow to lower values and if you throttle
the mass flow to lower values, this compressor is liable to go into stall.
Now, this difference between the maximum pressure point 2 and the design point 3 is popularly
or is generally known as stall margin, which you have done before in our lectures. This
stall margin, by design, needs to be comfortable to the operation of the engine.
The modern designers would like to make it as high as possible. If the design pressure
ratio can be pushed as high as possible, so that by design you create a stall margin,
so creating a stall margin, where the stall is and where the design is, design point operation
is, is indeed decided by the designer. This stall margin creation is, is the designers
job. It is, it does not happen, it is not be decided by the operator, it is not to be
left later on to be decided by operational schedule, it is built into the design of the
compressor, it has to be designed in. So, stall margin is something, that has to
be designed in and that makes the choice of design point a little more difficult. You
know, that you have to create so much of stall margin, which is indeed safety margin of operation
of the compressor and indeed, that of the whole engine. Because if the compressor stalls,
the whole engine is stalled, this is a problem. This is a problem, which the compressor designer
has to deal with right in the beginning, throughout the compressor design, that at no point of
operation of the compressor of the engine, the compressor should stall because if it
stalls, the engine is gone and this stall margin has to be created. As we shall see
later on, that this stall margin has to be created for each stage design of the compressor
because you would actually create a similar compressor characteristic for each stage.
If you have 10 stage compressor, we just saw a 9 stage compressor, 3 low spool and 6 high
pressure compressor, each of those 9 stages has a characteristic map like this and each
of these, those stages would have to have a comfortable stall margin of its own. All
9 stages together, the entire low pressure spool together. the entire high pressure spool
together would have a stall margin of its own.
So, you can have overall stall margin of the entire compressor, you can have a stall margin
of only the low pressure spool, you can have stall margin of only the high pressure spool,
you can have stall margin of each of those 9 stages and they have to be designed in.
They are not going to happen, you are not going to leave it just to happen, they have
to be designed in and that is the designer's one of the tricky and rather challenging jobs
of the compressor designer. So, finding the design point is one of the
tricky design decisions that need to be taken early on in the design. Sometimes you may
have the latitude to change the design point a little, but not much. When you are putting
all the compressors together, slight change in the design point may have to be adopted
to get the final design, but not much. So, choice of the design point is a tricky business.
Then, we come to the fixing of the initial design point parameters. What needs to be
done is, as I was just mentioning, that the entire multi-stage compressor needs to be
split up in individual stages. To begin with, it needs to be split up, may be in to 2 spools
or 3 spools; in many modern axial flow compressors are actually 3 spools.
So, you have to decide what the spools would do? How much the spools should perform? And
then, you need to decide what the individual stages should perform here? I have just tried
to give a very, you know, rough estimate or rough kind of numbers, figures, that would
allow the initial choice of the kind of performances, that you can ascribe or prescribe for individual
stages of a multi-stage compressor. Now, these numbers are decided by the state
of art of the design of these compressors. You see, the state of art is decided by the
design methodology that has been developed where we are today. We have talked about subsonic
transonic compressors; most aero-engines today do not use supersonic compressors. So, that
state of art of the compressor design has to be used to get these numbers when you are
initiating the design process. During the research, which you have to do
to create this design, you may try to push this design numbers to somewhat higher values,
in terms of pressure ratio or efficiency. However, that is going to be normally marginal.
So, I have tried to give some numbers here that gives you some idea, which means, in
the initial stages, you can actually get pressure ratios of the order of 1.4 to 1.8 by putting
in substantial amount of work. The temperature rise, that is shown here,
is of course the measure of the work to be done. delta t into CP is the per unit mass
flow work done and the efficiency, I have shown here, is of the order of 0.6 to 0.7.
You may like to push it to a little higher, may be difficult, if the initial stages are
transonic. Most of the modern aero-engine 1st stages
are transonic. Once you have transonic, as you have seen in earlier lectures, you have
shocks and the shock losses bring down the efficiency a little, and as a result of which
the efficiency of the initial stage are often a cut or two below the efficiencies, that
are possible with the subsonic stages. In the middle stages, the modern axial flow
compressors have indeed put their efficiencies to very high values. If they are subsonic,
you can indeed get efficiencies of the order of the 92 percent. If they are subsonic, you
may have to go below 90, 89 percent or 90 percent at the most, or 88 percent. Now, in
the middle stages, your efficiencies are normally a little on the higher side compared to the
initial stages, and one of the reasons is, in the initial stages, the flow often admits
flow through the intake, which has invariably certain amount of non-uniformity or certain
amount of unexpected non-uniformity. This is catered to by the design and if you do
that, you pay a very small penalty in the design efficiency, so that under non-uniform
inlet flow operating conditions, the efficiency of the initial stages do not drop very much.
So, to cater to such off-design vagaries of axial flow compressor operation, the efficiency
of the design point is sacrificed a little. This is a premeditated sacrifice, it is done
deliberately by the compressor designers and it is a well sacrificed, you know, choice,
because under various off-design operations, you still get good efficiencies of the order
of 84, 85 percent. This is a good compromise; however, in the
middle stages, you do not have those problems. The initial stages actually act almost like
a filter. So, the non-uniformities go away and the flow deliver to the middle stages
are often very uniform and hence, in the middle stages, you can aspire and prepare to design
compressors are very high efficiencies of the order of 91, 92 percent.
In the last stages, what happens is, the blades, as you have seen, become very small. When
the blades are very small, the three-dimensional flow that we have discussed earlier in this
lecture series engulfs the entire blade. And when that happens, many of the two-dimensional
airfoil theories, that we have discussed, do not really operate that way and hence,
the efficiency of the compressors suffers a little. So, the aerodynamic efficiency of
the compressors, aerodynamic losses actually go up and hence, it shows up in the efficiency
and hence, the last stage efficiencies are not as good as the middle stage efficiencies.
So, they are a cut or two below the middle stage efficiencies.
As we can see, the pressure ratio keeps going down through the stages, in initial stages
is very high; middle stages, it is low, down, and then in the last stages, it is very low.
No matter how much work you try to pump in, the flow is already at a very high pressure,
very high temperature and indeed very high density. So, from the fundamental thermodynamics
on aerothermodynamics, you know that working at very high pressure and temperature, you
can only affect very small change in density. So, that is what happens in the last stages.
So, the work done in the last stages is deliberately kept on the lower side because you are not
going to much profit out of pumping in lot of work and hence, the work done is somewhat
on the compromise side. Even to get that you have to actually put in a lot of work. So,
the last stages are normally the higher pressure spool, the high pressure stages, which normally,
as we know, ran at high speeds.
So, this initial parameter fixing essentially requires you to fix from continuity the mass
flow that goes to the compressors. Factor of change of mass flow may be taken between
HPC and LPT if you are catering to cooling of turbine. So, some amount of mass flow may
be taken out and of course, fuel is pumped into the turbine. So, different between turbine
mass flow and compressor mass flow has to be factored into the design. And then, from
work balance you decide what the compressor mass flow should be between the turbine work
and the compressor work and this is to be done separately for LPC and LPT.
And then, of course, you get the split between the fan and the HPC and as a result of which
you get the bypass ratio and then, you get the rotating speeds of the fan, the LP and
the HP spools. These, of course, mean that the compressor of fan speed has to be the
same order as the turbine speed. So, that something, which again has to come
out matching between the turbine and the compressor and the power balance between the compressor
and turbine fixes the compressor work, that has to be done. Of course, there are efficiencies
of the turbine, efficiencies of the compressor and the mechanical efficiency of the shaft
that comes into the picture in deciding how much work the compressor should do.
Having obtained this, you can now decide the amount of work to be done for the rotor of
the, individual rotor, individual stages. There are a certain parameters that normally
we talk about. The axial velocity is often normalized into
what is known as flow coefficient phi and this is normally kept less than 1. These are
figures that people have used over many, many years. So, actual velocity by U is normally
less than 1; the work done, that is being performed again is normalized by U square.
In some books it may be written as 2 U square and this gives us psi, which is the work done
coefficient and this work done coefficient is normally of the order of 0.5 or lesser.
In conventional compressors, in modern compressors, this is being pushed to higher values of the
order 0.7 or 0.8. So, the actual work done on the compressor
on individual stages is decided by first deciding on the work done factor of the individual
stages in the radial gap, that you can keep for the individual stages depending on which
stage you are considering. As we know, the radial gap in the last stages have to be,
you know, a little more than actually of the same order as the initial stages in terms
of, it is called, it is higher. So, some of those things would have to be
decided as we go along and then, of course, the fan loss, that occurs in big fans, all
that put together gives you some idea as a first cut idea. What, what should be the work
done or work supplied to the compressor compared to the amount of theoretical work that the
compressor needs to do from the fundamental two-dimensional blade theory.
Having decided this, you have to decide quickly the work done factor. As we see, the work
done factor goes down with the number of the stages. The first stage's work done factor
is very high, in the later stages, the flow is three-dimensional and the work done factor
is often somewhat on the lower stage, lower values.
So, that has to be also decided. These are pre-decided by the designer from earlier experiences
or earlier data that is available with the particular design group.
And then, of course you need to fix the initial parameters that mean, the work to be done
by the individuals stages. A conventional method is, if you have in a subsonic stage,
you can try to pump in certain amount of work; if it is transonic stage you can pump in certain
amount of work. So, the different between the work you can
pump in for a transonic stage and then of the, transonic, subsonic stage are slightly
different. Once you decide, that how much work you can possibly do stage by stage, then
you can get the number of stages. So, Z here is a first cord value of the number of stages
of a multi-stage actual flow compressor that allows you to arrange the stages and then
try to design the flow track. Now, you can go back and try to design your
flow track, so that you get a smooth flow track to begin with, of course, you may have
to come back here. If these stages are redesigned or re redesigned due to many other reasons,
then the flow track would have to be re smoothened back into a final smooth shape.
So, these initial parameters are fixed by deciding on the work done, the efficiencies
of the individual stages. And to make sure, that you have correct distributions, the pressure
ratio of all the stages put together must, of course, give you the overall pressure ratio
given by the engine designer. The density variation and the annulus area variation gives
you the flow track, which we talked about earlier and this, of course, from fundamental
aerothermodynamics and this annulus area's variation has to be kept smooth. This, sometimes
the axial velocity for the design may have to be used as a moderative parameter to give
you the smooth flow track. So, actual velocity is something, which the
designer may use; he may held it back and use it for design later on to moderate and
get a smooth flow track. So, this is how you get a first cut actual flow compressor configuration
and its distribution and its first cut smooth flow over a multi-stage configuration.
In the next, we will get into blade design, we will look at using the blade fixing, the
design point fixing, that we have done in this class. We will get into individual blade
design methodology, this is what we will doing in the next class, where you will be attempting
to tell you how to design rotors and stators of individual stages of a multi stage actual
flow compressor.