Hello and welcome to lecture number sixteen
of this lecture series on jet aircraft propulsion.
We have been talking about axial compressors
over the last few lectures, and we are going
to continue our discussion on axial flow compressors
today. And this would be the last lecture
on the theory of axial flow compressors, and
subsequently in the next lecture we are going
to discuss about we will basically have a
tutorial on axial compressors.
Now, what in today’s lecture we are going
to cover two very important aspects of axial
flow compressors. One of them is to do with
a very fundamental form of design of the axial
flow compressor blades, and the that is what
we will initiate our discussion on and subsequently,
we are going to discuss about the characteristics
performance characteristics of single and
multi stage axial flow compressors. And the
performance characteristics is a very important
part of axial flow compressor design, and
also it plays a very significant role in the
performance of the engine as a whole, because
the compressor is to be matched with the turbine,
and matching of the compressor and turbine
is in some way related to the performance
characteristics.
And that also reflects the performance of
the engine as a whole in the sense that performance
characteristics would tell us that what is
the band of operation for this particular
compressor where in the operation is safe.
And what happens, if we exceed these bands
of operation obviously, the performance is
going to degrade. And in some cases as we
shall see today.
The compressor might enter into might enter
into certain unstable modes of operation which
can effect, which can drastically effect the
performance, and working of an engine as a
whole. So, in this context it is very important
for us to understand the significance of performance
characteristics. So, but before that let us
discuss about a very fundamental, form of
or method of design of the axial compressors
in what is known as a free vortex deign, and
we will see what is the principle behind a
free vortex design, and why we need to consider
such a design methodology.
Subsequently, we will discuss about single
and multi stage compressors, and we will also
towards the end of the lecture discuss in
brief, about two instability modes of operation
of an axial compressor. These are known as
rotating stall and surge, so that we will
take up towards the end of the lecture. So,
we are going to discuss begin the lecture
today with discussion on what is known as
free vortex design. And in subsequently we
will take up the performance characteristics.
So, let us discuss about what is meant by
free vortex design, but before that let me
give you a background about what is meant
by a radial equilibrium basically radial equilibrium
is one of the conditions that needs to be
satisfied in the sense that all the flow parameters
in terms of velocity pressure etcetera, need
in the radial direction also needs to be considered.
In whatever design methodology or the velocity
triangle etcetera, which we have discussed
over the last few lectures, we have not really
considered variations of properties in the
radial direction.
We have assumed that in a particular cross
section the blade speed is a constant, the
tangential velocity is constant and many other
properties remain a constant. But in an actual
blade you know that the blade speed is going
to vary, all the way from the hub to the tip.
And so how do you consider or account for
this in a design methodology. So, radial variations
of all these properties needs to be considered
and factored into when we take up a serious
design of an axial compressor blade. And that
is one of the principles that will be made
use of in, what we will be discussing about
in free vortex design. So, for a realistic
design, what we need to do is to consider
radial variations of the following one is
of course the blade speed, which we know will
vary any way, from hub to tip because it is
a direct function of the radius. The other
parameter that we will need to be considered
is the axial velocity. Then the radial variation
in tangential velocity and static pressure.
So, if we have to maintain a reasonably uniform
flow at the compressor exit. And, why do we
need to maintain that we need to maintain
a uniform flow at the compressor exit. Because
the next stage or hum that is going to follow
a particular stage, will depend upon, what
is coming into the stage from the previous
one. And so, if there is a uniform flow that
exits one stage of an axial compressor. That
is also beneficial for these succeeding stages.
So, one of the ways of ensuring that we can
have a fairly uniform flow exiting the compressor,
is to ensure that there is a uniform distribution
of specific work input at each of the cross
sections that is starting from the hub all
the way to the tip. If we can maintain, or
at least try to maintain, relatively uniform
distribution of specific work in the radial
direction, then it possible that we should
be able to get a fairly uniform flow at the
compressor outlet, which is obviously good
thing for the succeeding stages.
Now, in order to ensure that we have uniform
specific radial work distribution. Now, we
know that the enthalpy difference across a
stage delta or even a compressor delta h not,
is equal to enthalpy thrice across a compressor
stage. That is equal to the product of the
blade speed that is U multiplied by delta
C W right that is something that we had discussed
in one of the earlier lectures that the ah
Enthalpy rise, specific enthalpy rise will
be equal to the product of blade speed times
the difference in the tangential velocity
between the inlet and exit. So, delta C W
is basically the difference in the tangential
velocity. So, if we equate this now we are
trying to maintain relatively uniform specific
work input. So, we should be able to get some
hints from this as to how we can do that.
So, we know that delta h not which is specific
enthalpy specific enthalpy change across a
stage is equal to blade speed times delta
C W or C theta. And, which is equal to omega
r, which basically the blade speed is the
product of the angular velocity times the
radius this multiplied by delta C W is basically
equal to the specific work input.
So, what does means is that for a given rotational
speed, that is if we fix omega then r times
delta C W must be a constant. So, the product
of the radius, and the tangential velocity
must be a constant. Now, this can ensure that
we can have for a given rotational speed;
we can ensure that the specific work is a
constant. So one configuration or one design
methodology, which can ensure that this is
satisfied is known as the free vortex design.
And in a free vortex design, basically we
keep the product r times C W it is kept a
constant that they exit for each of these
blade roles. And so, given the axial velocity
and the blade speed at different cross section
from the hub to tip we have axial velocity
and so on. And so, from hub to tip we know
all these parameters; and if we to if we were
to ensure that the product r times C W is
kept a constant. We can actually solve the
velocity triangle; all the way from hub to
tip.
So, in vortex design methodology that is one
of the basic principles trying to keep the
product r times C W A constant, which will
ensure that the specific work input, required
for this particular blade would be a constant.
So, if that is the case we can ensure that
r times C W is kept a constant.
Now, for example let us, take a look at one
example where in we can see what has happens,
if we were to maintain the velocity triangles
if we were to solve the velocity triangles,
keeping r times C W a constant. If we were
to do that; so let me repeat what I was saying
so, basically if we have r times delta C W,
which we are trying to maintain a constant
for different cross sections all the way from
hub to the tip. Then from axial velocity,
which is known at the inlet and blade speed
we can solve the velocity triangle.
So, let us take one example of, what would
happen if we were to take to do this, what
is shown here are three cross sections at
the hub the mean and the tip. And their corresponding
velocity triangles and if we were to use the
free vortex method for designing such a blade.
This is how the velocity triangles are likely
to look like.
This is just one example now let us, take
a look at the hub section, where we have the
velocity triangle at the inlet. And the exit
of the blade; so this particular velocity
triangle, which is shown here. C 1 is absolute
velocity entering the blade at the leading
edge at the hub v 1 is the corresponding relative
velocity. U is the blade speed; and at the
exit we have C 2, which is the velocity absolute
velocity exiting the blade and V 2, which
is the relative velocity exiting the blade.
And if you try to maintain r times C W constant;
we can see that the blade cross section well
the orientation of the blade itself changes
drastically as we move from the hub towards
the tip, which means that and we can see velocity
triangles at the mean; and also at the tip.
So, what you notice is that if you were to
is were to stag these different cross sections
from the hub all the way to the tip. You can
clearly see that the blade is going to be
twisted it is no longer going to be a straight
blade as we have been discussing so far, where
we can at least the velocity triangles we
have discussed in the last few lectures we
were seeing that the blades were little bit
straight. Now, here with the free vortex design
methodology we can see that the blade is no
longer going to remain straight.
It is going to have a fairly significant twist.
The other significant thing that you can try
and notice is that during our discussion on
degree of reaction. We have seen that when
degree of reaction is close to 0.5 or is equal
to 0.5. The velocity triangles, become symmetric.
So, that is something that you can probably
try to see here at the mean cross section
of the blade. We can see that the velocity
triangles are more or less symmetric. And
this is indication that the degree of reaction
here is likely to be close to 0.5, whereas
at the hub and the tip. It is quite different.
And, what comes out is that in most of the
design a processed that one would encounter.
The degree of reaction approaches zero close
to the hub; it becomes very low. And towards
the tip it becomes much higher than 0.5 it
might approach one, and even though we are
maintaining a degree of reaction of around
0.5 at the main section.
So, this is just an example of one case of
how we can use free vortex design methodology
to design a blade cross section, and there
of course, the other variants of this methodology,
which we shall discuss now. And by using certain
modifications to the free vortex design methodology
we can of course, arrive at other methods
of designing a blade.
Now, what is important in all the these methods
is that we need to satisfy the conditions
of radial equilibrium. That is the equations
of motion the three-dimensional equations
of motion needs to be satisfied.
That is one fundamental requirement in all
these design methodologies. So based on this
besides free vortex design, where in we have
r times C W is equal to constant there are
other methods like forced vortex, which is
r times C W is equal to a r square exponential
method which could be r times C W is equal
to a r plus b. And constant reaction, which
is r C W is a r square plus b, where a and
b are of course constants, and needs to be
fixed (( )).
So, these are other variants of the methods,
where in we can try to ensure a constant specific
radial work. And that is required, because
we would like to maintain a fairly uniform
set of properties in the exit of a particular
rotor blade. So, free vortex design basically
is one of the attempts or one of the methods
by, which we can try to ensure a constant
specific radial work criteria.
So, what we have discussed in brief for now
is one of the ways of one of the methods or
popular methods of design of an axial compressor
blade. And what we shall discuss next would
be as I discussed had initially. We should
be talking about the different performance
characteristics of single and multi stage
axial compressors.
So we will begin our discussion, with consideration
of a single stage axial flow compressor. We
will first discuss about performance characteristics
of single stage compressor, followed by this
we will be talking about the multi stage characteristics.
Now stage of an axial compressor as you probably
know by now compressors comprises of a rotor
and a stator. So let us, take up a characteristic
rotor and the stator and then we will discuss
about, how we can characterize this particular
rotor and see what happens as you change different
properties.
Now, we have a typical axial compressor stage
here, which consists of a set rotor blades,
followed by a set of stator blades. We have
already seen this velocity triangle (( )) on.
At the rotor inlet we have absolute velocity
entering at C 1 relative velocity at V 1 blade
speed is zero. And at the exit of the rotor
we have, absolute velocity is equal to C 2
and relative velocity is V 2. And blade speed
of course, remains the same its U. And this
velocity triangle is, what is basically goes
into the stator basically the absolute velocity
that enters the stator. And exits at velocity
of C 3 living at angle alpha.
So, here we can see as the as the flow enters
the rotor and exits the rotor. There is a
deceleration in terms of the relative velocity
and that is, what leads to the diffusion,
and similarly, as the flow enters the stator.
The absolute velocity decelerates from C 3
from C 2 to C 3 leading to diffusion.
So, the combined velocity triangle is something,
which we have discussed earlier as well. If
we were to overlap the two velocity triangles
at the inlet and exit of the rotor then we
get a combined velocity triangle with all
the angles indicated here as well. Let me,
just quickly go through these velocity triangles
we have, absolute velocity at an angle alpha
1 at the inlet, of the rotor and relative
velocity V 1 at an angle beta one at the inlet,
at the exit we have the absolute velocity
leaving the rotor at an angle alpha 2. And
relative velocity leaving the rotor at angle
beta two.
And C W 1 corresponds to the tangential component
of the absolute velocity C W 2 corresponds
to the tangential component of the absolute
velocity at the exit of the rotor. And similarly,
V W 1 and V W 2 are the corresponding relative
velocity components. Delta C W is the difference
between C W 2 and C W 1; and C a is that axial
component of the absolute velocity.
So, with this in mind from the velocity triangles
we can infer that C W 2 is equal to U minus
C a tan beta two. So, let see where that comes
from C W 2 is this component this should be
equal to U, which is the blade speed minus
the this particular component, which is what
is given by C a tan beta 2. So C a is this
component; C a times tan beta 2 is this component.
So, U minus C a tan beta 2 is C W 2 similarly,
C W 1 is C a tan alpha, C a C W 1 is this
so, C a tan alpha 1 is this component. Now
we also know that delta h not that is the
specific enthalpy rise across a stage should
be equal to U times delta C W. And delta C
W is C W 2 minus C W 1.
So, if you go to substitute for C W 2 and
C W 1 here, we get delta h not is equal to
U multiplied by U minus C a times tan alpha
1 plus tan beta 2 or delta C W by U is equal
to delta h not divided by U square, which
is 1 minus C a divided by U into tan alpha
1 plus tan beta 2. So, what we have here is
the specific work ratio or the stage loading,
which is expressed in terms of two important
parameters. One is the axial velocity; and
the blade speed and of course the angles the
blade the inlet angle alpha 1 and the blade
outlet angle. So, the specific work ratio
or the blade loading has expressed in terms
of two distinct parameters.
So, what this means is that if we go to change
the design mass flow rate; mass flow rate
is directly proportional to the axial velocity
C a. And so, if we change design mass flow
rate or the blade speed either of them is
going to effect the loading characteristics.
Because delta C W by U is equal to 1 minus
C a by U into tan alpha 1 plus tan beta 2.
So the stage loading is directly a function
of either the mass flow or the blade speed,
besides of course, the angle so if we were
to assume that the inlet angle angles are
fixed.
This means that the performance of the stage
will directly depend upon the mass flow, which
is in turn equal to the axial velocity or
the blade speed U. That is this ratio C a
by U plays a significant role in the stage
performance characteristic. So the blade performance
or stage performance is a direct function
of the ratio C a by U. And so, we have already
defined c a by U if you recall earlier on
we have defined C a by U as the blade loading
in terms of C a by U as we have defined in
the last lecture.
So, let us look at what happens as you change
C a by U. That is basically the flow co efficient
thus defined last slide. So, what we have
plotted here are two parameters one is the
stage loading. In terms of what we just now
derived delta h not by U square, which is
delta C W by U. And these stage efficiency;
so, delta C W by U is equal to delta h not
by U square that is 1 minus C a by U into
tan alpha 1 plus tan beta 2. So, if you were
to plot this for different values of the flow
co efficient C a by U. As we keep changing
the flow co efficient what happens to this
loading characteristics.
So, what we will see is the one we indicated
by this thick blue line refers to the measured
loading characteristics as C a by U is changed,
which could be either by changing the mass
flow or by the speed. So, we observe a characteristic
as shown here, which means that as we reduce
the mass flow the pressure rise or the stage
loading increases up to a certain point. And
then subsequently if we continue to reduce
the mass flow it will decrease. And this has
certain implications, which we will discuss
during the multi stage performance characteristic
as well. And so we see that at this point
that is indicated by C a by U which is corresponding
to the design condition. We have this particular
characteristic and if we were to look at the
corresponding stage efficiency. We get the
maximum efficiency around that point. That
is corresponding to C a by U design, which
is of course less than ah hundred percent
of there is a certain efficiency associated
with the stage. And if we were to draw a tangent
at this point were C a by U is given by this
point if you if you draw a tangent at that
point.
The slope of that is basically given by tan
alpha one plus tan beta two corresponding
to the design condition. So, this the slope
of this line basically is, what is given here
by tan alpha 1 plus tan beta 2 corresponding
to the design condition. So, what is shown
here is basically, how a particular stage
of an axial compressor is going to behave
as we change the mass flow or the speed.
So, in terms of either of them we have represented
them by the flow co efficient that is C a
by U. So as c a by U changes how is it that
the stage performance changes in terms of
the loading of the stage as well as the efficiency
of the stage. So what we see here is that
basically the measured performance and, how
it performs in terms of the efficiency corresponding
to C a by U design. So, what this means is
that the as one deviates from C a by U design.
The stage is not going to perform as it is
supposed to be for the design conditions.
So, what we will see next is for off design
conditions, where in C a by U is either greater
than C a by U design or C a by U is less than
C a by U design. How the performance of the
stage would get effected. So, let us take
a look at what happens in terms of the velocity
triangles as well as what happens on the blade
as we change the flow co efficient from its
design value.
So, as C a by U let us take a look at three
different cases here; the first case is, when
C a by U is actually equal to the design condition.
Then we have the stage performing normally
that is normal operation under design condition
of this particular stage. So the velocity
triangle with the relative velocity at entering
the stage at an angle beta one and absolute
velocity at C 1 C 1 entering at alpha one.
Now, let us consider the first off design
condition, that is if C a by U is less than
C a by U design. And if you assume that this
is only by reducing the axial velocity or
changing the mass flow alone keeping the blade
speed same. That means if we fix U and just
change the mass flow it means that for a lower
mass flow, how the stage is going to perform.
So, as C a is less than C a by C a design.
This means the axial velocity is now less
than the design axial velocity. As we reduce
the axial velocity what, happens is we see
that the velocity triangle getting altered.
So, this was the original velocity triangle;
and as we reduce the axial velocity the velocity
triangle has got altered. Because now, C a
by U is now less than C a design, which means
that the relative velocity will now enter
the rotor at angle, which now greater than
what it was at the design condition. So, here
beta 1 is actually greater than the beta 1
at the design.
So, therefore, it means that the flow approaches
the stage at a very high angle of incidence,
which is basically a positive incidence here.
There is a chance that the flow would separate
from the suction surface of this rotor.
So, there is flow separation occurring here
on the suction surface of this blade. Therefore,
this is basically a positive incidence flow
separation. The other extreme of this is C
a by U is greater than C a by U design, which
means C a is greater than C a design. If U
were to be fixed the blade (( )) is fixed
then there is a possibility that the incidence
is now negative. And there could be flow separation
from the pressure surface and that basically
means a negative incidence flow separation
flow might separate from the pressure surface
of the blade.
So, these are two extreme ah cases of operation
of the stage when the flow co efficient is
different from the design flow co efficient.
It is either less than design co efficient
or greater than if it is less than if the
blade fixed then C a is less than the design.
Axial velocity and the flow separates from
the suction surface might separate from the
suction surface leading to positive incidence
separation. And if C a is greater than C a
of design then it could lead to negative incidence
separation.
So, having understood some of the aspects
of a single stage performance characteristics
of an axial compressor. Let’s now move on
to multi stage axial compressor. That is if
there multiple number of these stages one
after another how does the performance, how
can we evaluate the performance of such an
axial compressor. Now, to do that we need
to understand, what are the different parameters
or variants or variables based on which we
can evaluate this performance.
So, at the outlet of the compressor we are
interested in two things one is the pressure
ratio; stagnation pressure ratio across the
compressor. And the other parameter is the
efficiency of this compressor. So, these are
two parameters, which we will be interested
in. And so, we will need to see what are the
other variables on which these two parameters
depend that is efficiency and pressure ratio
of the compressor expressed in terms of other
variables. So, that we can then go ahead and
then look at the performance characteristics.
So, for a multi stage compressor now we are
going to denote the inlet of the multi stage
compressor by station one. And exit by of
the compressor by two that means the overall
pressure ratio of the compressor is P 0 2
by P 0 1. So, the compressor outlet pressure
and efficiency isentropic efficiency is a
function of several properties several variables.
So it could be mass flow rate, the inlet stagnation
pressure, inlet temperature, the rotational
speed, the ratio of specific heats gas, constant
for the working fluid, viscosity of the working
fluid, the design of the blades themselves
and the diameter d. So, these are the different
parameters on, which the outlet pressure outlet
stagnation pressure and outlet efficiency
depend upon.
So, if you were to express this in terms of
non dimensional parameters, so if we carry
out dimensional analysis of these terms that
we have listed here. Then non dimensional
parameters come out to be on the left hand
side we have the stagnation pressure ratio
of the compressor, P 0 2 by P 0 1 and the
efficiency.
This is a function of mass flow rate multiplied
by square root of gamma R T 0 1 divided by
P 0 1 D square. The other parameter is omega
D by square root of gamma R T 0 1; then we
have the omega D square by viscosity mu. Then,
the ratio of specific heats and the design.
Now, for a particular design suppose we have
frozen a particular design and we can assume
that gamma, which is of this particular fluid
and the viscosity do not really affect the
performance significantly or do not change
much and for a given diameter of the engine.
Because, the diameter has been frozen the
diameter has also been frozen; and the gas
constant fixed. So this particular set of
non-dimensional parameters will now reduce
to P 0 2 by P 0 1. And the efficiency as a
function of m dot root t 0 1 by P 0 1; and
n times T 0 square root of T 0 1, where n
is the rotational speed.
So, the pressure ratio and the efficiency
of the compressor depends up on basically
two parameters here. One is corresponding
to mass flow rate and the other corresponding
to the rotational speed. And so, let us further
reduce it in terms of standard conditions,
which we will see that is known as corrected
mass flow and the corrected speed. So, pressure
ratio and efficiency as a function of mass
flow rate times the root of inlet stagnation
temperature divided by P 0 1, and the speed
that is n times square root of T 0 1.
So, we will further express them in terms
of standard conditions. That is standard ambient
pressure and temperature; so, that this performance
characteristics can be used in any other ambient
conditions. So, that once it is standardized
and corrected it can be used under other conditions
as well. So, if you process this further in
terms of standard day pressure and temperature.
When we have P 0 2 by P 0 1, and the efficiency
are functions of m dot square root of theta
divided by delta and N divided by square root
of theta.
Here theta is equal to T 0 1 divided by T
0 1 standard day. And delta is equal to P
0 1 divided by P 0 1 standard day, where T
0 1 standard day is 288.15 kelvin. And P 0
1 standard day is 101.32 kilo pascal.
So, if you go to express these performance
parameters in terms of the characteristic
of a compressor, multi stage compressor. So,
what I have shown here is one typical performance
characteristics of a particular axial compressor.
We have on the Y axis the pressure ratio P
0 2 by P 0 1 and expressed in terms of the
X axis that is mass flow rate m dot square
root of theta divided by delta. We also have
the efficiency; as a function of the mass
flow rate m dot square root of theta by delta.
So let us, look at the pressure ratio characteristics
first. So, typical compressor multi stage
axial compressor characteristic would comprise
of pressure ratio versus mass flow at different
speeds. So, these lines that are shown here
are for different speed ratios that is N by
square root of theta.
That is for different speeds of rotation how
the characteristic change. Let us, take up
one particular speed let us say .7. So, what
does this line mean is that as we change the
mass flow rate? As the mass flow reduces the
pressure ratio increases. And it reaches a
particular peak beyond, which the pressure
ratio, which is not show here. It will droop
or it will fall drastically. The reason by
I not showing ah the points on the left hand
side of the line, which is indicated as the
surge line is because after this point the
compressor operation is unstable. Because
of what is known as surge, which I will discuss
shortly what is meant by surge.
So, there is an instability in the compressor
performance, which prohibits the compressor
operation on the left hand side of this line.
So, compressor operation is possible; stable
compressor operation is possible; only on
towards the right hand side of the compressor
of this particular line. So the surge line
dictates one of the limits of the compressor
operation. And so, what performance characteristic
here shows how the performance in terms of
pressure ratio varies as we change the mass
flow.
We also have the efficiency characteristics
shown here how the efficiency changes as we
change the mass flow. So, we have peak efficiency
corresponding to the mass flow, which is shown
here, so far a particular mass flow at 0.85
speeds. We have the peak efficiency of occurring
at a mass flow somewhere around here. And
that is true for other mass flows as well.
So, mass flow versus efficiency, mass flow
versus total pressure ratio both of these
put together. Define the performance of a
multi stage axial flow compressor. Now, let
me take a closer look at the pressure ratio
versus the mass flow characteristic. So, you
might have noticed here that the peak efficiency
is occurring at a point, which is slightly
away from the surge line. And at the same
time I mentioned that operation on the left
hand side of the surge line is not possible,
because of the presence of instabilities.
So, we would like the compressor to be operating
at point at a safe operating point, which
is away from the surge line. So, what is shown
here is in terms of this dotted line corresponds
to the actual operating line of an engine,
which means we are really not operating very
(( )) we would not want to operate very close
to the surge line. Because there is always
a risk that the compressor might go into surge.
If there is a certain fluctuation in the mass
flow rate.
So, the engine the compressor is usually operated
or designed for operation along an operating
line, which is away from the surge line. And
the difference between these two points is
basically referred to as surge margin. So,
there is always a certain margin provided
between the engine operation and the surge
line, which indicates or denotes that there
is a certain margin provided for a safe operation
of the compressor. So, surge lines is one
of the extremes of operations of the compressor.
That the engine actually (( )) slightly away
from the surge line, which is known as the
engine operation line. So, the multi stage
performance characteristic as defined here
is in terms of the efficiency as well as the
pressure ratio. So, in some books and literature
you might also find that the efficiency plots
are shown in the same pressure ratio plot
as well so you will also find contours of
constant efficiency plotted on the same graph.
Now, I mentioned that the axial compressor
performance is limited by surge on one of
the sides. And that there is one of the instability
modes of operation of the compressor. And
so before I discuss surge let me talk about
yet another mode of instability called, which
is known as the rotating stall.
So, axial compressor performance is hindered
by two instability modes there of course other
modes as well. But primarily two modes of
instability one is known as the rotating stall,
and the other is known as surge.
Now rotating stall is a non axis symmetric
mode of instability. And on the other hand
surge is the axis symmetric mode of instability
and it is periodic, where as rotating stalled
is not necessarily periodic it is a periodic
in nature. But both of these modes of operation
eventually can hamper the performance of a
compressor drastically. So rotating stalled
basically involves progression around the
blade unless of a stall pattern. That is the
stall pattern progressively moves around the
annulus of the axial compressor, where in
one or more adjacent blade passages are instantaneously
stalled. And then the stall cell continuously
moves or progresses around the annulus of
the compressor. So, this means that the rotating
stall can lead to alternate loading, and unloading
of the of the blade, which means that there
is a possibility of fatigue failure eventually
if rotating stall mode was to be present continuously.
So, let us see what actually happens during
rotating stall. Now, during rotating stall
let us say there is a certain pocket of non
uniformity in the incoming flow. And this
pocket of non uniformity may cause a certain
one either one blade or a set of adjacent
blades to operate under stall condition. So
here we have a non uniform flow; that means
ah there is a flow entering the compressor
at a very high incidence than the design condition.
So, high non uniformity entering into this
particular set of blades causes this blade
let us say to get to be stalling, which means
that as this blade stalls. It also causes
the flow entering the second the adjacent
blade to enter at a higher incidence, because
the blades are actually rotating. So, there
is also a relative motion here the blades
rotate.
And, because of this the non uniformity now
progresses, and move towards the adjacent
blade. Causing the adjacent blade, also to
now stall you has this blade stalls it unstalls
this particular, which is earlier under stall.
Because the flow is now deflected in this
fashion here. And also because of the rotation
of the blades themselves.
So, this stall blade, which was undergoing
a stall. And this stall cell as you see here
moves towards the adjacent blades and the
new stall is now on this particular blade.
And eventually it unloads the previous blade,
which was undergoing stall. So, this continuously
happens and this stall cell moves progressively
moves from one end to another around the annulus.
And, what you can immediately see here is
that the direction of the rotation of the
stall cell is opposite to that of the rotation
of the blades themselves. So rotating stalls
cells ah rotate in a direction, which is opposite
to that of the rotor rotation. And you can
see the rotor rotation obviously for this
compressor is in the direction from right
to left. Whereas, the stall cell moves from
left to right. So similarly on a annulus you
can imagine that the rotating stall cells
will actually move in a direction opposite
to that of the rotor rotation.
So the rotating stall is in an instability,
which often precedes surge. And we will see
that a little later; and the stall patterns
will obviously move that in a direction, which
is opposite to that of rotor revolution. And
the frequency of the rotation of a stall cell
is of course, not fixed it can keep changing,
but it can be as high as about fifty percent
of rotor frequency.
And rotating stall may usually be initiated
by the presence of a non uniform flow (( )) rotor
blades. So, what I have shown here are three
different modes of operation of the stall.
One is that rotating stall may be affecting
only a part of span. This is the annulus of
the compressor; this is the hub, and this
is the casing. So, rotating stall may be affect
part of the span or it may be a full span
stall. That it affects all the way from the
hub to the tip. And eventually it may lead
to surge, where in the entire annulus undergoes
ah stall. So, this means that the rotating
stall is one of the precursors is likely to
be one of the precursors of the surge. That
is one of the rotating stall were to continue
and progress leading to full annulus stall.
It may eventually lead to surge.
So, which brings us to what is meant by what
is actually meant by surge, we have already
seen surge line is seen in compressor characteristic,
which was on the left hand side. On one of
the limits of compressor operation and I mentioned
that you cannot really operate the compressor
beyond the surge line. Because of the occurrence
of surge itself. So, let us understand what
we mean by surge. Now, surge is surge line
is obtained as by joining all the points on
the speed lines of compressor, where surge
is likely to occur. So, surge line is the
locus of all the points of a multi stage axial
compressor.
Surge basically, involves fluctuation of fluid
back and forth along the annulus. Axial fluctuation
of the fluid of the working fluid. And the
entire annulus of the compressor is affected
by surge, which is why I mentioned that surge
is axis symmetric. That is the entire annulus
of the compressor is affected by a separating
flow. And it is violent oscillation of the
fluid back and forth. So, the onset of surge
can lead to very drastic effects on the compressor,
and as the engine as a whole. Because compressor
is feeding in to the compressor chain bar
(( )) and the turbine and so on, which means
that if there is something drastic happening
compressor. It will immediately affect the
combustion chamber and therefore, the turbine
which means the whole engine gets affected
as a result of surge.
So surge is characterized by violent and periodic
oscillations in the flow. It might lead to
flame blow out in the combustion chamber.
Because if there is a back and forth movement
of fluid in the combustion in the compressor.
It can lead to a flame out a flame blow out
in the combustion chamber. And obviously it
can lead to substantial damage of compressors,
which is why surge is something that always
needs to be avoided. Designers always try
to keep a safe margin between the surge line
and the operating line, which is basically
known as the surge margin.
I mentioned that there is a certain margin
provided between the surge line and the engine
operating line. And this is basically referring
to this surge margin. And so designers would
always like to keep a certain margin there.
So now, let us try to understand what is actually
meant by a surge; and let me take up the performance
characteristics once again we have the mass
flow in terms of the flow co efficient I have
taken at only one stage of the compressor
here.
We have flow co efficient and the pressurized
co efficient, what happens to the stage performance
as we keep changing the mass flow. Now, let
us say we have the stage characteristics,
which have been plotted here and in solid
line. And the throttle characteristics in
terms of these dashed lines, which means that
as we throttle the compressor as we reduce
the mass flow.
The throttle characteristics keeps changing.
And this particular stage let us say operating
at point a. As we throttle the compressor
will continuously move towards the left. And
it keeps moving along these dotted lines.
A to B and to C D and so on, but beyond a
certain point what we see what are indicated
by the points here with dash. That is D dash
C dash and B dash are those points, which
corresponds to unstable operation of the compressor
And why is it exactly unstable, because what
happens here is that as we reduce mass flow
in on the right hand side of the particular
line. Let us say, after on the right hand
side of E. As we reduce the mass flow it is
accompanied by an increase in the pressure
ratio. Whereas, on the left hand side we have
as we reduce the mass flow rate. It also result
in reduction in pressure ratio which means
as the pressure ratio reduces the pressure
downstream is lower than the pressure in the
upstream.
And so, that can lead to sudden fluctuation
in the mass flow rate. And that is, why operation
on the left hand side of what is given here
as the throttle characteristic can lead to
an unstable operation of the compressor. So,
what happens really here is that beyond this
point, which is given here as the tangent
of the stage characteristic any point on the
left hand side of this, where this stage characteristic
will have a positive slope. We mean that reduction
in mass flow will be accompanied by ah reverse
flow, which can fluctuate back and forth.
Because momentarily would have a lower pressure
of upstream than the downstream, which means
that there would be a reverse flow.
And as the flow moves from the downstream
stages to the upstream stages. There is a
decrease in pressure downstream as compared
to upstream and then this continues in a cycle
leading to rapid fluctuations in the flow
back and forth. So, this is what leads to
what is meant by surge, where in there is
violent oscillation of mass flow back and
forth. And something that can be explained
using the stage characteristic and the throttle
characteristic.
So, as we change the throttle characteristic
from extreme left hand side right hand side
as shown here. As we keep throttling, which
means it indicates some increase in flow resistance.
We obtain different performance characteristic
as denoted here by these points. But all these
points as you can see have a negative slope.
Whereas, as the stage characteristic reaches
a point, where in the slope is positive.
That indicates that these are the points where
basically the operation of the compressor
is unstable. And ah this is what is reflected
in the multi stage characteristic as well.
So, what I had shown was one particular line
here. And beyond this as you can see the slope
will have will be basically positive. Whereas,
on this side will be negative. So, operation
of the compressor is safe on all these lines
and all these points, where the slope is positive.
And the locus of all these points together
constitute what is known as the surge line.
So, operation of the compressor is unstable
on the left hand side of the surge line. Whereas,
it is safe to operate the compressor on the
right hand side ah of this surge line. So,
surge is basically the one of the modes of
instability of an axial compressor, which
is something that the designer would always
want to eliminate and avoid.
And rotating stall is one of the possible
one of possibly one of the precursors of surge.
And that is something that would eventually
lead to the occurrence of surge. So, let me
wind up today’s lecture, where in we were
discussing the about two important aspects.
One was the stage characteristics, the single
stage characteristic as well as the multi
stage performance characteristics of the axial
compressor. And the other aspect that we were
discussing was the free vortex theory we started
the lecture today with some preliminary discussion
about the free vortex theory.
And how it can be used for in preliminary
design of the axial compressors, subsequently,
we started discussing about single stage characteristic.
And how we can ah how we can basically evaluate
the performance of a single stage by relating
the flow co efficient to the pressure rise
or the stage loading.
And subsequently, we discussed about multi
stage performance characteristic in brief.
And then we also discussed about two modes
of instabilities. One is known as the rotating
stall, where in the stall cell progressively
moves around the annulus. We then saw that
rotating stall can eventually or if allowed
to continue may lead to occurrence of surge
as well, where in the entire annulus of the
compressor undergoes flow separation or flow
reversal.
And there could be rapid oscillations or fluctuations
of the flow, which could also lead to extensive
damage to the engine as a whole. So, single
stage multi stage performance characteristic
the significance of that and also the free
vortex theory. These were some of the topics
we had discussed in today’s lecture. And
what we will take up for tomorrow’s well
for the next lecture would be basically a
tutorial.
On axial compressors and we will wind up our
discussion on axial compressor with the next
lecture, which will basically be a tutorial.
We will try to solve some problems pertaining
to axial compressors. And also we will have
a few exercise problems, which we can solve
based on the discussion in the lecture. So,
let us take up these topics for discussion
in the next lecture.
