Hello and welcome to lecture number eleven
of this lecture series on turbomachinery
aerodynamics and today, we are on the eleventh
lecture of lecture series and we are
going to discuss a very important aspect of
axial flow compressors today. And in today’s
class, we are going to talk about performance
characteristics of single and multistage
axial compressors and the reason why I said
it is very important is because performance
characteristics are extremely important information
that are required by designers and;
obviously, for the engine designers as a whole
because it is the compressor performance
which determines the limits of operation of
the engine itself. That something which we
are going to discuss in today’s class which
means that the limit of operation of an entire
aero engine will in some sense be dictated
by the compressor performance itself. That
is
beyond certain levels, the compressor cannot
operate and that will puts a limit on the
engine operation itself.
And hoping that in the previous few lectures;
seven or eight odd lectures which you have
undergone so far, you must have had a fairly
good amount of information about two
dimensional as well as three dimensional aspects
of flow through axial compressors. So,
today’s lecture is kind of an over view
of the whole thing with out of course, looking
at
what is happening on the blade at individual
stage level, but trying to find out how
certain compressor which has been designed
is going to perform when the operating
conditions change. So, as the operating conditions
of the compressor changes, how does
a compressor react to such change in operating
condition?
So, that is the aspect of discussion which
we going to take up in today’s class. So,
we are
going to talk about two distinct aspects which
are related to performance characteristics
of axial compressors. We will begin with the
discussion on a single stage axial
compressor performance and we will extend
that to a multistage axial compressor. They
are the basic trends are identical for both
of them, but they are distinct differences
between what happens in a single stage axial
compressor as compared to a multistage
axial compressor. So, these are two aspects
of compressor performance that we going to
discuss in today’s class.
We will start with a single stage axial compressor.
Now you might be aware that a stage
of an axial compressor is constituted of a
rotor and a stator. So, rotor precedes the
stator.
So, a rotor and stator combination together
put together is what is known as a stage of
an
axial compressor and it is this that we are
going to analyze in today’s lecture on how
we
can estimate the performance of a single stage
and how the single stage performance
varies as the operating conditions change.
So, in today’s class, we will basically
be
talking about single and multistage axial
compressor characteristics. Let us start with
the
single stage axial compressor.
So, I mentioned that a combination of a rotor
and a stator put together is a stage. So,
this
is this these put together constitute a stage
of an axial compressor and this is what we
shall analyze and see how the performance
changes as the operating conditions of this
particular stage changes.
So, to understand that better, let us construct
the velocity triangles. Now this is the inlet
velocity triangle for the rotor. The air is
entering at an angle of C1 absolute velocity,
relative velocity is V1 which enters this
blade at tangential direction. Blade rotates
at a
peripheral speed of U. This is the velocity
triangle at the inlet of the rotor and this
is the
velocity triangle at the exit of the rotor.
Here velocity leaves the rotor at an a velocity
of
V2 which is again tangential to rotor, C2
is the absolute velocity leaving the rotor,
U is
the blade speed and C2 is going to be the
velocity with which the flow enters the stator
So, the velocity leaving the stator is C3.
There is no relative component for the stator
because the stator is stationary. Relative
component is true only for rotating components
like a rotor and that is why we have relative
velocities at the inlet and exit of the rotor.
So, this a typical axial compressor stage
comprising of rotor and a stator and we will
see
how we can estimate the performance or what
are the parameters on which the
performance of this single stage axial compressor
would depend upon and for which, we
will need to analyze the velocity triangles
a little more carefully. So, if we look at
the
velocity triangles little closely and also
mark the various velocity components on the
velocity triangle, we get velocity triangle
combination like this.
So, this is the velocity triangle at the inlet
and exit put together. Since the blade speed
is
common for both the rotor entry and rotor
exit that is the common point here. This is
the
inlet velocity triangle comprising of C1 V1
and angles alpha1 and beta1. At the exit we
have C2 V2 and angles alpha2 and beta2.
The corresponding velocity components are
Cw1 which is the tangential component of
C1. Cw2 is the tangential component of C2.
Vw1 is tangential component of V1. Vw2 is
the tangential component of V2. Ca is the
axial component of absolute velocity and delta
Cw is the difference between Cw2 and Cw1.
Delta Cw is important as we have seen in
earlier, because the power required to drive
the compressor primarily depends upon delta
Cw. So, since the power require depends primarily
on delta Cw, that is why in the
analysis that will the change in tangential
component will play significant role.
Now, from these velocity triangles, what we
can see is the at the exit Cw2 should be
equal to U minus Ca tan beta2 and Cw1 is Ca
tan alpha1. Let us take a look at the
velocity triangle. Cw2 is this component.
Cw2 is U minus Ca tan and beta2 and similarly
Cw1 which is this component is basically equal
to Ca tan alpha1 and since the net
change in enthalpy; that is delta h naught
is equal to U times delta Cw, we have delta
h
naught as U times delta Cw which is U minus
Ca times tan alpha1 plus tan beta2 or delta
Cw divided by U is equal to delta h naught
by U square is 1 minus Ca by U into tan
alpha1 plus tan beta2.
So, what we see here is that, we get a parameter
which is in terms of the delta Cw to the
velocity ratio which is a function of certain
angles which come from the velocity triangle
tan alpha1 and tan beta1; the axial velocity
and the peripheral speed. So, these are certain
parameters which will kind of influence. This
parameter of delta Cw by U, the
significance of which is what we will discuss
very soon, that how this that this ratio delta
Cw by U will play any role in the performance
characteristics. So, what we see from this
equation that we have now derived is that,
the performance of a single stage axial
compressor will depend upon a certain set
of parameters. One of them of course,
becomes is the axial velocity the blade speed
and the angles.
So, this means that any change in the design
mass flow rate; obviously, will affect axial
velocity Ca and change in rotor speed; obviously,
affects U. So, change in either Ca or U
will change the inlet angle beta1 because
let us go back to the velocity triangle here.
So,
if either Ca or U changes, it will cause a
change in beta1 and; that means, that the
blade
performance is strongly a function of this
ratio Ca by U. That is this ratio of axial
velocity to the blade speed will significantly
affect the blade compressor performance.
And it can be deduced that the stage performance
is a function of three parameters; the
loading coefficient psi, the flow coefficient
phi, and the efficiency. That is, there are
three parameters which of course, will also
include the flow coefficient which is Ca by
U. Besides Ca by U, the performance will depend
upon the loading coefficient and also it
will depend upon the efficiency of the compressor.
So, there are three parameter significant
parameters on which a single stage axial
compressor performance will depend; loading
coefficient which is denoted by psi, flow
coefficient which is Ca by U and the efficiency
eta. So, these are parameters on which a
single stage performance will depend. Now
when you go to a multistage as we will later,
on the host of other parameters which will
also be playing a significant role in the
performance which of course, we will discuss
in later slides. Now if I were to plot the
loading coefficient which was delta Cw by
U with reference to the flow coefficient and
also the efficiency with reference to flow
coefficient, let us now look at how that affects
the performance. Before I go to that, let
me also emphasize this particular point that
the
flow coefficient Ca by U is in some sense,
a measure of the mass flow rate. Because
mass flow rate is directly a function of the
axial velocity Ca and rotational speed of
course, being fixed, the mass flow rate is
directly proportional or flow coefficient
is
directly proportional to the mass flow rate.
So, as the compressor is throttled or mass
flow rate is changed, it changes the flow
coefficient. Similarly for the same mass flow
rate, as the speed is changed that also
changes the flow coefficient or Ca by U. Similarly
the loading coefficient will depend
upon how this mass flow rate is changing.
So, there is a dependence of the loading
coefficient delta Cw by U on the flow coefficient.
There is also a dependence of the
compressor efficiency on the flow coefficient.
So, let us now take a look at how these
two parameters change as flow coefficient
changes.
So, if I were to plot, let us take a look
at loading coefficient first. So, I have loading
stage
loading on the y axis which is delta h naught
by U square which is also equal to delta Cw
by U. On the x axis, we have Ca by U which
is the flow coefficient and we have seen
this expression, we have derived this delta
Cw by U is equal to delta h naught by U
square is 1 minus Ca by U into tan alpha1
plus tan beta1.
So, there is direct correlation between the
loading coefficient and the flow coefficient.
If
you were to plot this variation, you should
expect it to be a linear line. That is what
is
given by this dotted line here. One would
have expected a linear variation of Cw by
delta
Cw by U with the flow coefficient. Of course,
in an actual practice what is shown here is
given by the solid line that is the measured
performance? You can see the measured
performance is not necessarily a linear variation.
It is equal to the design point at which
the compressor has been designed which is
Ca by U design at which both the measured
and the actual is the ideal are the same.
At any other point, you can see that the
performance is different from what it has
it is supposed to be. And if you were to draw
it
tangent basically the actual performance,
the slope of this line is basically given
by this
angles; tan alpha1 plus tan beta1 toward the
design point.
So, this is basically giving this flow which
comes from this equation here. So, what is
to
be noted here is that, as the flow coefficient
changes from the design point, it also affects
the loading coefficient correspondingly. So,
there is a change in loading coefficient.
There is a deviation of the loading coefficient
from the design as the mass flow rate or
the flow coefficient changes. Now if we similarly
look at this stage efficiency, the stage
efficiency also has a similar variation with
reference to the ideal performance. Stage
efficiency would have approached in efficiency
of 1 for a Ca by U design and since
when it is actually operating, the stage efficiency
deviates from the design point and
there is a variation in stage efficiency as
compared to the design point variation. So,
there
is also a difference of the stage efficiency
or dependence of stage efficiency on the flow
coefficient. Similarly there is a strong dependence
of the loading coefficient on the flow
coefficient.
So, there are three parameters as we have
seen which kind of dictates the single stage
performance. The first parameter is the stage
loading coefficient which also has a
dependence on the flow coefficient phi. Then
we also have the efficiency which again
depends upon phi in some sense that, as phi
varies that affects the efficiency as well.
So,
these are parameters which drastically affect
a single stage performance. Let us now look
at what happens as we change the mass flow
rate or as the ratio Ca by U deviates from
the design point. At the blade level, how
does it affect the performance, what happens
to
rotor performance as Ca by U changes from
its design point.
So, for that we have the velocity triangles
for three different cases which have been
shown. One is a design condition and two off
design conditions. The design condition
which is normal operation, we have Ca by U
is equal to Ca by U design. This is the rotor
blade and we have flow entering the rotor
at an angle of V1 which is relative velocity
at
an angle of beta1.
So, this is the velocity triangle at the inlet,
V1 at an angle beta1 to axial direction, C1
at
an angle of alpha1 and a blade speed of U.
So, this is when the flow coefficient is equal
to flow coefficient at design condition. Now
if let us say, for a constant speed, the mass
flow rate is reduced, then this means that
this ratio Ca by U also reduces and this
necessarily an off design condition. When
Ca by U is less than Ca by U design that is
axial velocity is now decreases for same U.
So, keeping U fixed, if we reduce axial
velocity because mass flow rate is reduced,
it leads to an increase in beta1 and as beta1
increases beyond a certain angle, it leads
to what is known as positive incidence flow
separation. So, there could be flow separation
taking place on the suction surface of the
rotor blade. So, this is a suction surface
of the rotor blade. There will flow separation
from the suction surface when beta1 is greater
than beta1 design which occurs when flow
coefficient is less than flow coefficient
design. The other counter part of this off
design
condition is the negative incident separation
which will occur when Ca by U exceeds the
Ca by U design. That is when Ca is greater
than Ca design for constant U, beta1 becomes
very low and as beta1 decreases there could
be chances of flow separation from the
pressure surface of the blade of the rotor
blade. You can see that flow as separation
from
the pressure surface of the rotor blade and
this basically a negative incidence flow
separation. So, both these cases of flow separation
can occur either positive incidence or
negative incidence separation when you know,
the flow coefficient is different from its
design value. When flow coefficient is lower
than design value, it leads to what is known
as positive incidence separation. When flow
coefficient is greater than the design value,
it may lead to negative incidence flow separation.
So, this is how the performance of a single
stage compressor can vary. You have
dependence on three parameters; the loading
coefficient, the flow coefficient and the
efficiency and as flow coefficient changes,
we have seen how it affects the performance
of a rotor and there are two extreme cases
possible. You may have a positive incidence
separation when the flow coefficient is much
lower than the design value, leading to flow
separation from the suction surface of the
rotor and negative incidence separation which
occurs when the flow coefficient is greater
than the design flow coefficient, leading
to
flow separation from the pressure surface
of the rotor blades and these are two different
possibilities wherein the performance of the
compressor can be drastically affected. We
have also seen how phi versus psi and loading
coefficient versus flow coefficient
changes and how efficiency changes with the
flow coefficient.
Now having understood the single stage performance
characteristics, we will now
proceed towards a multistage axial compressor
and see how a multistage axial
compressor performance changes or varies as
the operating conditions change or what
are the parameters on which a multistage axial
compressor performance will depend
upon. So, multistage compressor as we know,
consist of a series of stages of axial
compressor which means you will have a several
combinations of rotor stator and if you
put all of them together, that constitutes
a multistage axial compressor. And what we
are
going to do is that, we will denote the inlet
station of a multistage compressor by station1
and exit of the compressor by station2.
Therefore, the overall pressure ratio of the
compressor, we will denote as P 02 by P 01
where P 02 is the compressor outlet pressure
and P 01 is the compressor inlet pressure.
So, the compressor outlet pressure P 02 and
efficiency will depend upon several physical
parameters or variables. So, we are going
to look at what are these different parameters
or variables on which the performance will
depend. So, we will list all these different
parameters on which the performance of a compressor
is going to depend.
So, let us list all these parameters and what
we see is that, P 02 which is exit stagnation
pressure and efficiency were is a function
of these mini parameters and what are these
parameters? We have mass flow rate, inlet
stagnation pressure, inlet stagnation
temperature, rotational speed omega, the ration
of specific caves gamma, the gas
constant R, viscosity of the air, then the
design itself and the diameter D. So, these
are
the different parameters on which the pressure
ratio will depend. So, now, if we nondimensionalise
these parameters, we can do that using Buckingham
pi theorem probably
have learnt about phi theorem earlier on.
So, if you non-dimensionalise this and express
these parameters in terms of non-dimensional
clusters, then we have P 02 by P 01 and
efficiency; both of which are functions of
these mini non-dimensional parameters which
is one of them is mass flow rate time square
root of gamma R T 01 divided by P 01 D
square. Then we have omega D divided by square
root of gamma R T 01, then omega D
square by new, then gamma and design.
So, these are anyway non-dimensionalise. So,
the other non-dimensional parameters are
these three. Now for a particular design,
we can safely assume that gamma and new do
not affect the performance significantly.
Similarly D and gas constant are fixed. So,
since
D is fixed, gas constant R is fixed, design
is fixed, new is fixed and the gamma are fixed.
These non-dimensional parameters can be simplified
and expressed as P 02 by P 01 and
efficiency are functions of m dot root T 01
by P 01 and speed as N by root T 01. So, here
we have the pressure ratio and efficiency
expressed in terms of two distinct parameters.
I
will still not call them non-dimensional because
if you look at the dimensional, if you if
you look at the dimensions of these two parameters,
they are strictly not nondimensional. That
is because we have taken off other parameters
which would have
indeed made it non-dimensional. P 02 by P
01 pressure ratio and efficiency are functions
of two parameters, one is mass flow rate time
square root of T 01 by P 01, the other is
speed divided by square root of T 01.
And so; that means, that there is one parameter
which is a function of mass flow rate,
other parameter which is function of speed.
So, pressure ratio and efficiency are
functions of mass flow rate and the rotational
speed. We will further simplify this and
see how the performance changes. We will take
a look at how the pressure ratio changes
as mass flow rate changes and speed changes.
How efficiency changes as mass flow rate
and speed changes. But the bottom line is
that the performance of axial compressors
multistage axial compressor in terms of pressure
ratio and efficiency can be expressed as
functions of two distinct groups; one is to
do with mass flow rate that is m dot root
[P 0
1] T 01 by P 01 and the second parameter is
N by root T 01 which does not make it nondimensional
because there were other parameters which
we have neglected for a given
design like the diameter D, gas constant and
so on.
Now, let us simplify this expression further.
What is normally done is that the
temperature and pressures are expressed in
terms of standard day pressure and
temperature. We will non-dimensionalise temperatures
and pressure with reference to
standard day conditions. Therefore, P 02 by
P 01 and efficiency can be expressed as
functions of m dot root theta by delta and
N by root theta. Here theta should be equal
to
T 01 by T 01 standard day and delta is stagnation
pressure divided by stagnation pressure
of a standard day. So, here theta and delta
refer to temperature and pressure ratios for
a
standard day. I will explain the significance
of why this non-dimensionalization is also
is
required for temperature and pressure. Basically
because when we are designing a
compressor for a particular condition, one
normally designs it for a certain ambient
condition, but this compressor may be operating
in an engine which is used in an
ambient condition which is entirely different
from what it has been designed for.
So, what is the guarantee that this compressor
is going to perform the same way as it has
been designed for a different condition?
So, the way to account for this is to express
the pressure and temperature in a nondimensionalised
form and so usually this is also referred
to as corrected pressure and
corrected mass flow rate and corrected speeds
because mass flow rate has been corrected
for the standard day pressure and temperature.
So, even if let say the engine is operating
at a temperature and pressure which is drastically
different from what it has been
designed for, because of this correction it
can partly take care of this variation in
pressure
and temperature. So, with this background
that we had so far on how we can express the
performance of multistage compressors, we
will now proceed towards looking at how the
variation of a compressor performance itself
is expressed.
So, basically a compressor performance variation
is also referred to as performance map.
So, compressor performance is expressed in
the form of a map and performance map
forms a significant part of a very significant
role in the design of an aero engine or for
that matter any gas turbine engine because
as I mentioned, a compressor performance
puts limits on the whole engine performance
as a whole because they certain limits of
operation for a compressor beyond which it
cannot operate or there are instabilities
which are introduced.
Therefore an engine will not be able to operate
satisfactorily beyond these operating
ranges and that is why a compressor map forms
a very significant input for an engine
designer who will need to know, what are these
limits between which this compressor is
going to operate. That is if I am designing
an engine and I will need to know that this
compressor has certain limits in terms of
mass flow rate and pressure ratio. So, this
is
amount of limit that I have during which between
which the engine has to operate
because beyond that the compressor cannot
operate and therefore, the engine as whole
will not operate at all. And therefore, compressor
performance map will form a
significant input for an engine designer who
will need to know what these limits are.
So, compressor performance is expressed in
terms of two parameters; as a function of
the
mass flow rate. So, one the parameters which
we are interested is what is a pressure ratio
developed by the compressor. So, the pressure
ratio P 02 by P 01 expressed as a function
of mass flow rate m dot root theta by delta.
And similarly what is this variation with
different speeds. As speed changes that N
by root delta or N by root theta, how the
performance changes. This is one of the parameters
which we are interested in. The other
parameter is variation of efficiency with
the non-dimensional mass flow rate and the
non- dimensional speed how the efficiency
changes.
So, I will now show you one typical compressor
map which basically tells us how this
variation can be tracked. Now if you look
at what is shown here, I have a typical
compressor map which is shown here.
On the y axis, we have P 02 by P 01 and efficiency
x axis we have mass flow rate which
is expressed in terms of m dot root theta
by delta where this is the temperature standard
day ratio and this is the pressure ratio standard
day with reference to standard day and
they are series of course, which you will
see and each of these lines correspond to
constant speed line and the speeds are expressed
in terms of N by root theta and that is,
as the speed changes, as you change the speed
of the compressor from very low speed
where this ratio will be close to 0 and as
you keep increasing that and it approaches
the
actual speed the design speed which is 1.
You can see that initially the speed lines
are flatter. As you look at compressor
performance at lower speeds very low speeds,
one would see a flat variation rather flat
variation of the pressure ratio with mass
flow rate. That is as mass flow rate changes
pressure ratio also changes, but that is over
a wide range. But as the speed increase as
we
go towards higher and higher speeds, the speed
curves become sharper and sharper. For
example, if you look at this speed curve at
N by root theta is equal to 1, you can see
that
speed curve is extremely sharp. And therefore,
the pressure ratio varies drastically with
mass flow rate, but that is over a very narrow
range of mass flow rate, beyond which
there is certain line which is shown here
a dotted line of course, there is curve beyond
this also, but that is a curve which a designer
would never want his engine to operate on.
I will explain what the curve is a little
later. Now I what you will notice is that,
as the
speed increase from very lower speeds and
as we proceed towards higher and higher
speeds, the performance curve which was initial
flat starts becoming sharper and sharper
to the extent that at very high speeds, that
is the design speed of 1, the curve becomes
very sharp; which means that there is a very
narrow range of operation of the compressor
here. And the sharp curve we are basically
means that mass flow rate does not really
influence or for the pressure ratio versus
mass flow rate is kind of a constant here
and
this basically refers to what is known as
its choking point, where you are trying to
pass
the maximum mass flow rate which this compressor
can generate.
So, beyond which mass flow rate does not change
much and there is a significant drop in
efficiency which I will come to little later.
So, what does line here means is that, under
this operating condition, even if we change
the mass flow rate substantially, there is
a the
variation in pressure ratio is very drastic
for a very narrow change in mass flow rate,
beyond which the pressure ratio drops as you
try to operate the compressor for mass flow
rate beyond that because mass flow rate is
fixed. You might recall the concept of
choking which you would have learned in your
gas dynamics solid fluid mechanics that
under certain operating conditions, mass flow
rate attains a peak level and mass flow rate
becomes maximum.
This is exactly in the case that is happening
here, that maximum mass flow rate has taken
place and no further mass flow rate can be
passed through by this compressor and if you
try to pass more and more mass flow, what
will happen is that it will effect two
parameters; one is the pressure ratio which
drops and also the efficiency which drops
drastically.
So, the curves which are shown here are the
efficiency curves for the corresponding
speeds. So, for lower speed as expected, one
would see a flatter efficiency curve and as
the speeds approach 1, the efficiency curves
also becomes sharp just like the pressure
ratio curves and you can see that the change
in efficiency is very drastic and very narrow
as the speeds approach the design speed. Now
on this each design line or in each speed
line, you can see multiple points which have
been shown here. These are the different
operating points of the compressors.
So, compressor may be operating on any of
these points or in between these points. So,
when a designer embarks upon designing a compressor,
what he does is that he tries to
design it for a particular operating condition
and then one would also need to evaluate
what happens when the compressor is going
to operate in conditions which are different
from what it has been designed for or what
are known as off design conditions. For an
aero engine for example, the design the operating
conditions can vary so drastically that
the designer has to ensure that even if the
off design condition is it its extreme, the
compressor still operates safely. Because
as you have seen here in the curve, on the
left
hand side there is a dotted line which has
been shown on the pressure ratio versus mass
flow rate. There is dotted line which is shown
and it is indicated as surge line. Now what
is surge is something we will discuss in detail
in a later lecture, but let me tell you that
the compressor operation is affected drastically
affected by two instabilities which are
likely to occur. One is known as rotating
stall and the other is known as surge.
Both of these are instabilities which can
drastically affect the performance of the
compressor to the extent that if surge occurs,
the compressor may fail and lead to flame
blow out in the commercial chamber and the
engine may shut down if the compressor is
surging.
So, the left, the dotted line shown on the
left hand side of the pressure ratio versus
mass
flow rate curve is sort of a limit for operation
of the compressor. That is, though if you
extend that line, you will still see a line
on the left hand side, but that is a line
on which
you just cannot operate the compressor because
that is a region of instability for the
compressor. The compressor cannot operate
in a stable manner if it is on the left hand
side of what is known as the surge line.
So, if compressor tries to operate on the
left hand side, it would undergo what is known
as surge during which the entire operation
of the compressor breaks down and engine as
a whole gets affected drastically and it might
lead to failure of the compressor and engine
shut down. So, surge is the phenomenon which
can affect the performance of a
compressor drastically. So, let me take a
closer take you to a closer look of what is
the
surge line and how it affects the performance.
Now the same performance curve that you saw
here, pressure ratio versus mass flow rate
is being shown in a better way here. Now here
we have the speed lines which are these
different lines which are shown. The surge
line is shown here and what is also shown
is
the engine operating line. Now engine operating
line is the line which is something that
the designer would like to use and how does
one at arrive at the operating line?
Operating line is the line through which the
engine is accelerated from 0 speed all the
way to design speed. Operating line would
ideally have to be a line where the efficiency
is maximum because you would always like to
operate the compressor in a condition
where it as maximum efficiency. If you join
all those points ideally, join all the points
maximum efficiency, you can get the ideal
operating line, but it may so happen that
many a times the maximum efficiency is very
close to the surge line which is a risky
affair because if you are operating very close
to the surge line, any off design operation
might push your engine into surge. That is
a risk which the designers are not willing
to
take, will not absolutely be willing to take
because that is too higher risk to be taken
to
operate the engine very close to this surge
line.
So, the engine designer always wants to a
keep a certain margin between the operating
line and the surge line. This is known as
the surge margin. Surge margin is a certain
margin or buffer which the designer wants
to put for the engine to ensure that even
if the
engine undergoes an off design operation,
a transient operation, the engine still does
not
touch the surge line. Because if the engine
were to indeed were towards the surge and
touch the surge line, that can lead to catastrophic
effects which are something which the
designer will always want to avoid.
So, surge margin is something which is kind
of a protection for the engine provided by
the by the designer to ensure that the engine
does not reach the surge condition even if
there is an off design operation of the engine.
And most of the modern day engines have
inbuilt surge warning systems and mechanism
which will prevent a pilot from accidently
operating the engine in a such way it can
surge.
So, the modern day computer which operates
an engine which is also known as the
FADEC that is the full authority digital engine
control, basically has inbuilt functions
which will prevent a pilot from making such
mistakes that will lead to surge of an
engine. And even if there is a possibility,
the surge warning sensors which will give
a
warning to the pilot saying that there is
a possibility that the engine can surge if
you
operate it so and so.
So, in this operating multistage compressor
performance map, there are two distinct lines
that we should be a familiar with; one is
of course, the surge line, the other is the
operating line. Operating line is the line
on which the engine is designed to be operating
for.
There is also another line which may not be
that significant. That is on the right hand
side right most side. You may also join all
those points on the right hand side to achieve
what is known as the choking line. Choking
is not really significant for a compressor,
but
it may be significant for a turbine which
we will see later on because turbines usually
operate under choked condition. So, that we
will discuss a little later when we take up
the turbines. For a compressor, the choking
line is not really a matter of that concern,
but
they could still be a line which represents
choking in axial compressor.
So, surge line and operating line; two distinct
parameters or lines that we need to be
aware of. Now based on these parameters that
we have discussed, we will now look at
how the performance changes as let us say
mass flow rate changes which we have also
seen for a single stage compressor. We have
seen that as the flow coefficient changes
from the design condition, it drastically
effects the performance of a stage. Let us
also
look at how flow coefficient changes can affect
the performance of a multistage axial
compressor.
Now, in multistage axial compressor, the problem
is that a small departure from the
design point in the first stage can cause
progressively increasing departure from the
design from the first stage onwards. That
is, a small reduction in the ratio Ca by U
at the
design point at the first stage could lead
to positive incidence separation at the last
stage.
Similarly a small increase in Ca by U design
could lead to negative incidence separation
in the last stage. And the most extreme mismatching
of these front and rear stages occurs
during starting. Now during starting what
happens is that the compressor has just about
began rotating.
So, as that rotation begins, the net change
in density across the compressor is not very
significant. So, change in density from the
first stage to the last stage is insignificant.
So,
there is hardly any change in the densities.
So, what happens as a result of that is that
as
the density changes are not very high, whatever
changes occurs at the inlet can have a
very significant effect on what is happening
at the exist.
So, there is a very significant effect of
the flow from the inlet all the way to the
exit and
this is especially through during starting
when the density development has not really
taken place. Its the pressure ratio and the
density changes have not really been initiated
because the compressor has just about the
started.
So, we will take a look at what happens during
starting what happens to the flow
conditions or velocity triangles for the inlet
or the first stages and what happens to the
flow velocity triangles at the exist or the
last stages.
So, I have two sets of velocity triangle here;
one corresponding to the first stages and
one
set corresponding to the last stages. What
is shown here by the dotted line correspond
to
the design velocity triangle.
So, these dotted lines are supposed to be
the so called design velocity triangle and
what
happens is that, in the first stages, axial
velocity to the ratio of Ca by U is lower
than
what it should be for design condition. And
what happens in the last stages is that Ca
by
U ratio is higher than what it is for the
design condition because mass flow rate is
fixed.
Now mass flow rate being fixed, the area is
fixed and the axial velocity is only parameter
which can change because density is also fixed
during starting.
So, from the inlet to the exit, if you have
seen an axial compressor geometry, the area
progressively reduces. From the inlet at the
inlet you have large area and that area
progressively reduces and you have a smaller
and smaller area at the exit. Since the area
is reducing, density is fixed for a constant
mass flow, axial velocity has to increase.
That
is what is happening during starting. Now
once it starts and the compressor operates,
the
density increases and this problem does not
take place once the compressor has is fully
operational.
So, this is basically a problem which occurs
during transient operation during starting
of
the compressor. So, what happens in this case
is that there are few stages in the
beginning where Ca by U ratio is lower than
the design ratio which means in first few
stages may encounter positive incidence separation
and towards the last stages Ca by U
is greater than Ca by U design and it may
lead to negative incidence separation in the
last
stage. There is a huge mismatch between the
initial stages and the later stages and that
happens just during starting.
So, how can we overcome this problem? So,
there are different ways of overcoming this
problem and what basically happens is that.
A decreased Ca with alpha1 and beta2
constant results in increased alpha2 and beta1
and similarly it leads to increase in loading
in both rotor and stator. Similarly case of
increased Ca, it leads to an opposite defect.
So,
there are different ways in which designers
have configured for self starting of
compressor. One of the ways is to use bleed
valves which will allow some of the
incoming air to escape.
So, this is the most common way one of the
common ways of elevating this problem,
that is use of the blade valve some way mid
way between the multi stage compressor that
will allow some of the mass flow rate to escape.
So, as the mass flow rate escapes, later
stages will have lower mass flow and therefore,
it will have Ca by U ratios which are
closer to the design value and therefore,
the problem of a extreme mismatch between
the
initial stage and the later stage does not
really happen. Other way of course, is to
use
variable guide mains which can change the
inlet angles, flow angles to ensure that the
flow is matched to the design Ca by U values
and the third option is of course, to use
multi spooling which is probably the most
common thing which is used now, that is you
spit the compressor into different stages
so that the later stages of operates at different
speeds as compared the initial stages which
is why most of the modern day engines have
multiple spools. It could be twin spool or
a three spool engines and therefore, you have
initial fan followed by low pressure compressor
and then a high pressure compressor
which are driven corresponding by different
stages of turbines.
So, these are different ways of trying to
ensure that the compressor operation specially
during starting is also taken care of and
there are no extreme mismatch is taking place
between the first few stages and the last
stages of multistage axial compressor.
Now, besides this, I mentioned that there
are two distinct problems or instabilities
which
can affect compressor performance. One is
known as rotating stall as I mentioned and
the
other is known as surge.
Now we will discuss in detail about rotating
stall and surge in a later lecture. Let me
just
give you a just quick introduction to what
is mean by rotating stall and surge.
Rotating stall is basically a non axisymmetric
phenomenon and it is aperiodic. So, it is
not a periodic phenomenon. Surge on the other
hand is axisymmetric which means it
affects the entire annulus of the compressor
and it is periodic. Rotating stall is basically
a
progression around the blade annulus of a
stall pattern in which one or more adjacent
blade passages are instantaneously stalled
then cleared for unstalled flow as a stalled
progress. Rotating stall obsessively causes
alternate loading and unloading of blades
may
be leading to a fatigue failure, but it is
not fatal. Surge on the other hand is a low
frequency oxidation of the entire annular
flow and it is periodic, but it leads to it
is a kind
of fetal phenomenon for the engine because
onset of surge can almost always lead to
engine failure and therefore, surge is much
more severe phenomenon as compared to
rotating stall.
Now, let me just go to the pressure ratio
versus mass flow characteristic to explain
this
little bit more. Now in this pressure ratio
versus mass flow characteristics, on the left
hand side that you see here is what is meant
by surge. When though theoretical there is
a
curve which extents, if you draw this curve
on the left hand side you still extend their
way, but a practical limitation in terms of
initiation of surge will prevent compressor
from operating on this side of the curve and
that is why this is known as the surge line
and it is important that they clearly demark
it between the surge line and the engine
operating line.
So, that is why there is a clear difference
between engine operating line and the surge.
Rotating stall is often considered to be a
precursor to surge, that is as the engine
approaches the surge line, there is a possibility
that rotating stall initiates and rotating
stall then allow to proceed further and propagate
further, can evolve into surge and the
engine can eventually lead to surge, but rotating
stall is something which can be
prevented and controlled, but surge once initiated
is very difficult to control and that is
that is why designer would also always want
to avoid that the engine even approaches
surge.
So, surge is something that we will need to
be avoided and under all circumstances and
that is why it is important that the designer
understands the surge margin very well. We
will discuss details of surge and stall, that
is instabilities in detail in one of the later
lectures.
So, let me conclude today’s lecture where
we have discussed about very important aspect
of performance characteristics of axial compressors.
We began our lecture today with
discussion on the performance of single stage
characteristics and extended that to multi
stage characteristics. We have seen that pressure
ratio for single stage; its the loading
coefficient versus the flow efficient and
efficiency versus flow efficient that one
would
be interested in. In a multi stage characteristics,
we have pressure ratio versus mass flow
rate non-dimensional mass flow rate as a function
of different speeds which is also nondimensionalized
with the temperature and efficiency versus
mass flow rate at different
speeds. So, these are different parameters
based on which one can construct the
performance characteristics or performance
map of multistage axial flow compressor.
So, these were the topics that we have discussed
in today’s lecture. So, I hope you have
been able to grasp some of the effects of
aspects of performance characteristic and
what
is the significance of performance map of
an axial flow compressor. So, these were the
topics which we have discussed in today’s
lecture and we will continue discussion on
instabilities and in flow conditions and their
effect on performance of axial compressor
in future lectures.
