Hello 
and welcome to lecture number thirty-one of
this lecture series on turbomachinery
aerodynamics. We have discussed quite a lot
on different aspects of turbo machines over
the last several lectures. We actually started
off with very introductory topics and very
fundamentals of some, the turbo machines,
starting with thermodynamics and its analysis
as applicable to turbo machines.
We then moved on to discuss about axial compressors
and we had quite a lot of
discussion, detailed discussions on axial
compressors and the various design aspects
of
axial compressors and how an analysis, the
detailed analysis of axial compressors can
be
carried out. Subsequently, we spend some time
on discussion on turbines and we first
started off with the axial turbines, the design
issues related to axial turbines, performance
analysis of axial turbines and so on.
What we going to discuss today is a slightly
different topic in the sense, that the, the
component that we are talking now about is
not really an axial turbo machine. We are
going to discuss about centrifugal compressors
starting from today's lecture and we will
continue with this on 2 more lectures. We
will discuss some details about centrifugal
compressors, but in contrast to axial compressors,
our discussion would be rather
superficial in the sense, that we will not
be really taking up very detailed discussion
on
the design aspects of centrifugal compressors.
The basic reason being, that centrifugal compressors
are not really widely used in
modern day aircraft engines as compared to
the axial compressors. They are still used,
but they are, their usage has been limited
to rather smaller sized aero-engines and some
other applications. And that is the reason,
why we shall not really be discussing too
many
details about, especially to do with design
aspects of centrifugal compressors. But of
course, we will spend some time discussing
about the fundamental issues related to
centrifugal compressors, the different aspects
of analysis of centrifugal compressors, as
well as the performance characteristics in
quite some detail, over the, over the next
2 or 3
lectures. Also, of course, we will also be
having a tutorial session, where we will get
a
chance to solve some problems associated with
centrifugal compressors.
So, in today's lecture, we will start with
the fundamentals, we will talk about the
thermodynamics of centrifugal compressors
and subsequently, we will be discussing
about the different elements of centrifugal
compressors. What are the different
components, which constitute a centrifugal
compressor, are and what is the flow
characteristic associated with the flow through
these different components?
So, let us begin our discussion with the thermodynamics
of centrifugal compressors, but
of course, we will also have a quick introduction
to centrifugal compressors as a whole.
And see, what centrifugal compressors are
and why are it, that these compressors are
not
really used in that much popularly as compared
to the axial compressors? So, that two
distinct aspects of centrifugal compressors.
As we can see, thermodynamics, as well as
the components of centrifugal compressors,
so it will be very interesting to know, that
centrifugal compressor, in fact, has a longer
history than axial compressors.
In fact, the earliest jet engines that flew,
one by Frank Whittle in, in England and the
other, where German engineer named Fanzhoean,
both of them developed the jet engine
independently and both these initial developments
of jet engines used centrifugal
compressors. In fact, that continued for a
very long time and even do the, the, the very
common aircraft, which were used, the fighter
aircraft which were used during the 2nd
world war, all of them had, in fact, most
of them had centrifugal compressors.
There are certain inherent advantages with
centrifugal compressors, but of course, the
disadvantages are also equally substantial
and that is the reason why, as we look at
larger
and larger sized aero-engines, use of centrifugal
compressors becomes rather
disadvantageous, in the sense, that centrifugal
compressors require a larger frontal area.
That, is probably the most important disadvantage
of the, of a centrifugal compressor,
that the pressure ratio, that is developed
per stage from a centrifugal compressor, very
much depends upon the overall diameter of
the jet of the centrifugal compressor, which
means, that if you look at a larger sized
aero-engine, which is used in, let us, a modern
day passenger or fighter aircraft, they all
require the thrust requirement from such an
engine is tremendous. And to be able to develop
such a high level of thrust, it is
necessary, that the compressor develops the
corresponding pressure ratio required for
developing or generating this kind of a thrust.
From a centrifugal compressor if you were
to develop such a high level of thrust, the
frontal area required by such an aircraft
of such a compressor would be substantial.
And
obviously, such an engine would also have
a huge amount of drag.
So, an aero-engineer, an aircraft, airframe
engineer would not really want an aero-engine
with a large frontal area because that is
going to increase the overall drag of the
aircraft
and obviously, that is not a good idea. And
so, if you compare this with an axial
compressor, to develop the same pressure ratio
and axial compressor requires a smaller
frontal area, but of course, axial compressor
requires multiple stages to develop the same
pressure ratio.
Centrifugal compressors can generate far higher
pressure ratio per stage as compared to
axial compressor and that is of course one
advantage, a huge advantage of centrifugal
compressor, that they can generate a large,
much larger pressure ratio per stage than
an
axial compressor.
We will, we will of course, be exploring the
reasons for this a little later. When I will
explain thermodynamics of centrifugal compressor,
we will see that centrifugal
compressors have a slightly different mechanism
of pressure rise than axial compressor.
And that is the reason why they can generate
much higher pressure ratios per stage.
Yet, there is a yet another difference or
disadvantage, so to say, between centrifugal
and
axial compressor. For larger sized engines,
axial compressors have slightly higher or
better efficiencies than centrifugal compressor
and that is, of course, if you look at an
aero-engine perspective, the efficiency is
of utmost importance and even a slight
improvement in efficiency means a big deal
in terms of the overall engine performance.
And therefore, that is where axial compressor
scores yet again over centrifugal
compressor and these are primarily the two
reasons, why centrifugal compressors are not
really used in larger sized aero-engine.
They are used very much in smaller sized engines
because for smaller engines, axial
compressors, in fact have certain disadvantage,
because as you reduce the engine overall
diameter to smaller and smaller levels, the
losses associated with tip clearance and so
on
increased substantially. And therefore, in
fact, for smaller sized engines, centrifugal
compressors may have performance or efficiencies
as high or in fact, even better than
axial compressors. And so for smaller engines,
it is a common practice to use centrifugal
compressors and therefore, smaller sized engines,
which are used in, let us say business
jet or smaller airplane, they still have engines,
which have centrifugal compressors.
So, to sum up, centrifugal compressors obviously
can generate much higher pressure
ratio per stage. They, obviously, have larger
frontal area and therefore, they are not as
commonly used as axial compressors and of
course, they are little less efficient.
And centrifugal compressors are used in auxiliary
power units, the APUs of many
aircraft. Some aircrafts also have a centrifugal
compressor as part of the air conditioning
system, which is used in the aircraft and
in some engines, centrifugal compressors are
used in combination with an axial compressor,
that is, centrifugal compressor would
form the last stage of a set of axial compressor
stages and such engines are also quite
popularly used, which are of course the medium
or smaller sized engines; some
examples being the T700 from GE, PT6 from
Pratt & Whitney or the Annie Wetly 53
engines.
So, these are some engines, which have centrifugal
compressors, which are used in
combination with an axial compressor, and
the, the inherent advantage here is, that
one
axial compressor can replace multiple centrifugal
compressor stages because it is
possible to generate a higher pressure ratio
per stage by a, from an axial, from a
centrifugal compressor as compared to axial
compressor. And that is why, having a
centrifugal compressor as a last stage would
actually replace several axial compressor
stages, and that is a big advantage because
it leads to a lot of saving, possible savings
in
weight and part count and so on. So, there
are some advantages of trying to do that kind
of a configuration.
So, let us now take a look at some typical
centrifugal compressor rotors. So, I have
here
two different types of rotors, the one you
see on the left hand inside is a so called
classical centrifugal compressor rotor, which
has a straight radial blade. You can see,
this
is the impeller of the centrifugal compressor
and you can see, that these blades are radial
and straight, and of course, there is a bend
here, at what is known as an inducer. We will
discuss little more details about this later
on. So, an inducer actually turns an axial
flow
and guides it into the impeller and makes
the flow radiant.
On the right hand side, you can see, any,
the rotor of a centrifugal compressor, which
is
much more complicated than what you see on
the left hand side and this is a rather recent
development. And you can see that these blades
are much more complicated than what
you see in a conventional centrifugal compressor
rotor. And you can also see that at the
exit of the impeller, you, these are the diffuser
vanes, of course that is not really shown
here, these also would have diffuser vanes.
So, these are the vanes of the diffuser and
of
course, we will discuss more details on why
a diffuser is used in, in a centrifugal
compressor.
So, having understood or at least please take
a look at two different classes of centrifugal
compressor rotor. Let us take a look at the
schematic and understand what constitutes
a
centrifugal compressor.
So, there are primarily 3 distinct components
in centrifugal, in a typical centrifugal
compressor. It has an inlet and followed by
a rotor, which is also referred to as an
impeller in a centrifugal compressor and the
impeller exhausts or discharges the flow
into what is known as a diffuser, and from
the diffuser there is a collector or a volute,
which guides the flow towards the outlet.
So, the flow enters the impeller in an axial
direction and then, the impeller deflects
the
flow and turns it into a radiant flow and
this radial flow exceeds or exhausts the rotor,
exhausts the compressor through the collector
or volute.
And most of the impellers also have, what
are known as, inducers. Inducers basically,
guide an axial flow and allow the flow to
enter the impeller smoothly in the absence
of
inducer as we will see later, the flow can
actually, say, there is a tendency for the
flow to
separate from the impeller vanes if one does
not have any inducers. So, inducer is sort
of
like an inlet guide vane that we have seen
in the case of an axial compressor.
So, there are, there is a, there is a set
of stationary components as well as one rotating
component in a centrifugal compressor. The
impeller forms the rotating component or
the rotor of a centrifugal compressor. The
inlet and the diffusers are the stationary
components of stator of a centrifugal compressor.
So, once we have an, so now, that we have
understood the, the working or basically,
the
components are constituents of a centrifugal
compressor, let us now try to understand the
operation of the centrifugal compressor from
a little more fundamental sense, from a
thermodynamics perspective. We will try to
understand what really happens as the flow
passes through these different components
of a centrifugal compressor.
Now, I had shown the, the other three distinct
components, which I had marked as 1, 2
and 3. Let us take a look at them once again.
1 is here being referred to as the inlet of
the
centrifugal compressor; 2 is the diffuser
and 3 is the exit of the diffuser or the volute
or
collector of the centrifugal compressor.
Now, on a T-S diagram, this is temperature
entropy diagram, you can see, that of course,
it looks quite complicated here. Let us try
to understand what are, what is basically
being
implied by the set of a constant pressure
lines that are shown here.
So, station 1, as we have seen, is this inlet
of the compressor; 2 correspond to the diffuser
and 3 is for the exit of the diffuser or the
volute. So, there are static pressure lines
as well
as the corresponding total pressure lines,
which have been shown. Energy is added, as
you know, in the impeller and so the stagnation
pressure rise takes place between 0 1 and
0 2 pressure, between stations P 01 and P
02. And in the volute, there is a stagnation
pressure loss that is why you can see, that
there is a certain amount of loss, which is
being associated here because of the loss
of stagnation pressure in the volute.
Now, from station 1 static pressure rises
between station 1, P 1 to P 0 1 and this is
the
corresponding stagnation parameters, C 1 square
by 2 C p. So, T 1 plus C 1 T 1 is T 1
plus C 1 square by 2 C p. There is no change
in stagnation temperature between station
2
and 3 because there is no energy added after
the impeller. So, energy is added between
station 1 and 2 and that is why, we see a
change in stagnation temperature from T 0
1 to
T 0 2, where, that is where the energy is
added.
And actual process they are shown in 2 different
lines here. There is a thicker one, which
is showing the process between 0 1 and 0 2
and there is another line, which is showing
the process between, 0 2 and, 0 1 to 0 3.
So, it, it is possible of course, that in
some
centrifugal compressor, there may not be a
vane less, could be or may not really have
this vane less space between the inducer of
an impeller exit and the diffuser, and that
is
why these two distinct lines have been shown.
But of course, they both lead to the same
stagnation temperature; there is no change
in
stagnation temperature here. If we were to
look at the losses, which are in, occurred
in
centrifugal compressor, then the total losses,
as shown here, is between the stagnation
temperatures, which it would normally achieve
minus the stagnation temperature that it
should have achieved if the process was isentropic.
So, this is corresponding to the process if
the whole were to be isentropic and in which
case, there are, of course, no losses taking
place. And so, the corresponding dynamic
parameters are also shown here between station
for, let us say, station 3, between P 3 and
P 0 3. We have c 3 square by 2 C p and C 2
square by 2 C p between which basically,
takes the temperature from d 2 to T 0 2.
So, if you look at, if you compare this with
the temperature entropy diagram that we had
discussed for an axial compressor, you will
see, you can quickly figure out the
similarities between both these compressor
operations, at least in a thermodynamic
sense. In, even in an axial compressor we
have seen that energy is added in the rotor
and
you may actually have a total pressure loss
taking place in the stator. Even though static
pressure continues to rise in the stator,
one may have total pressure loss taking place
because of frictional effects.
So, they are quite similar in the sense, that
in, in the case of centrifugal compressors
also
we have an impeller or the rotor, where energy
is added and that is followed by a
diffuser, where there is obviously, no more
energy addition taking place.
One may have, one continues to have static
pressure rise, which is why P 3 is actually
greater than P 2, but there could be some
amount of total pressure loss taking place
in the
diffuser due to frictional losses and, and
that is why, we have P 0 3, which is less
than P
0 2.
So, what we will do next is to look at the
working of the centrifugal compressor, as
well
as trying to estimate the work done or work
required for driving centrifugal compressor
rotor, and we will relate that to the velocity
components; very similar to the analysis we
have done for an axial compressor as well.
We will try to relate the work done or work
required for driving the compressor to the
velocity components because it would be easy
for us to construct the velocity triangles
and develop and calculate the work done or
work required for a centrifugal compressor.
So, let us look at the governing equations
for centrifugal compressor stage. Now, in
a
centrifugal compressor rotor, the torque required
for or torque applied on the fluid by the
rotor is a function of the mass flow rate
of course, and components of the tangential
velocity. So, here, we have torque required
is equal to m dot into r times C w at station
2
minus r times C w at station 1 and so here,
the stations 1 and 2 are denoting compressor
inlet and outlet respectively.
Unlike an axial compressor where the, there
is hardly any change in these tangential
velocities between, for a given station, here
what we will see little later as well, that
even
the blade speed is not really a constant because
the flow is a radial; the blade speed also
changes with every radial location.
And so, we have mass flow rate m dot m dot
times the r m, the velocity component,
tangential velocity C w at station 2 minus
r times C w at station 1. So, the total work
done per unit mass is w, is basically a function
of the rotational speed omega times the
torque divided by the mass flow rate. This
is in turn equal to omega times r times C
w at
station 2 minus times C w at station 1. So,
if U, multiply omega times r, we get the blade
speed U. Therefore, work is equal to U times
C w at station 2 minus U at C U times C w
at station 1.
And so, in axial compressors we had actually
written this as U times delta C w because
U at inlet and exit of the compressor was
assumed to be the same. Here, it, it does
not
remain the same and it changes with, because
the flow is indeed radial.
Now, if you now look at the energy equation,
the steady flow energy equation and
compare that with what we have written here
for a centrifugal compressor rotor, we have
work is equal to the change in enthalpy stagnation
enthalpy, h 0 2 minus h 1, this is equal
to the static conditions and the dynamic conditions.
So, h 2 minus h 1 plus C 2 square by
2 minus C 1 square by 2.
We have already calculated the change in enthalpy
stagnation enthalpy in the previous
equation here. So, if you substitute that
here, we have h 2 minus h 1 is equal to w
minus
this velocity changes, where w has already
been calculated as shown here. So, h 2 minus
h 1 change in static enthalpy is equal to
U times C w at station 2 minus U times C w
at
station 1 minus C 2 square by 2 plus C 1 square
by 2, where C 1 and C 2 are the absolute
velocities entering the rotor, entering the
compressor and leaving the compressor
respectively.
Now, if you look at the impeller for example,
let us take a look at the schematic of an
impeller and we have an impeller inlet tip
radius, as shown here, as r 1 and impeller
outlet radius as r 2 and the corresponding
blade speeds would be u 1 at this location
and
u 2 at the exit of the impeller.
The velocity components for an impeller, then
the above equation, which we have
written earlier, that is, h 2 minus h 1 is
the difference of U times C w at station 2
minus
U C w at station 1. And the velocity components,
that gets transformed into h 2 minus h
1 is U 2 square by 2 minus U 1 square by 2
minus the relative velocities V 2 square by
2
minus V 1 square by 2. So, this in differential
form, we can write as dh is equal to d into
omega square r square by 2 minus d into V
square by 2.
Now, if you recollect the basic thermodynamics,
the Tds equation, Tds is also equal to
dh minus dP by rho and therefore, we have
on the left hand side dh, we shall replace
by
dP by rho. For an isentropic process Tds is
0, so dP by rho is equal to d into omega
square r square by 2 minus dV square by 2
minus Tds, which for an isentropic flow
becomes 0. Therefore, dP by rho is d into
omega square r square by 2 minus d into V
square by 2.
So, what we have just now written down is
an expression, which relates the pressure,
change in pressure across a compressor, two,
two distinct parameters or terms. One is
proportional to the rotational speed and the
radius or radial location, the other is
proportional to the change in relative velocity.
Now, this is a generalized form of an equation,
that I have written down, which also
could be extended to an axial compressor,
in which case we have assumed, that there
is
no, there is no change in the axial, well,
the radial location for given analysis. So,
if you
take up one radial plane, then there is no
change. The d omega square r square term
becomes basically 0 for an axial compressor,
which means, that the pressure rise would
now be equal to minus dV square by 2 for an
axial compressor, that is, the pressure rise
in an axial compressor is proportional to
the amount of deceleration taking place at
the
compressor in the relative velocity, in terms
of the relative velocity?
But in an a centrifugal compressor, as we
have just seen, the pressure rise is a function
of
one additional parameter, which is d of omega
square r square by 2, that is, even if there
is no deceleration taking place in a centrifugal
compressor rotor, which means, that if the
2nd term is, is equal to 0, one can still
at in a certain amount of pressure rise simply
because of the 1st term, that is, d omega
square r square by 2.
That, it is possible to achieve pressure rise
in a centrifugal compressor even if there
is no
deceleration taking place, which means, that
centrifugal compressors ideally should not
be affected by boundary layer flows because
we are saying, that even if there is no
deceleration taking place, one can still achieve
pressure rise because of the centrifugal
effect and that is why, it is called the centrifugal
compressor.
But most of the modern centrifugal compressors
also have a certain amount of the
deceleration taking place, that is, pressure
rise also because of deceleration or diffusion
as well as because of displacement of the
centrifugal flow field.
So, there is a component of both in a centrifugal
compressor and which is why, even
centrifugal compressors are indeed affected
by boundary layer flows, and it is not
possible to eliminate the boundary layer effects
all together, even in a centrifugal
compressor, but of course, it is possible
to achieve much higher pressure ratios per
stage
in a centrifugal compressor as compared to
an axial compressor.
So, in an axial compressor, where we can assume,
we have assumed the d r, that is
change in the radius is equal to 0.
The equation, that we have written here, dP
by rho is d omega square r square by 2
minus dV square by 2 is simply reduced to
dP by rho s minus dV square by 2, that is,
in
an axial compressor rotor, the pressure rise
can be obtained only by the decelerating the
flow. In a centrifugal compressor, the first
term is basically greater than 0 because omega
square r square by 2, change of that is always
greater than 0.
Therefore, pressure rise can be obtained even
without any change in relative velocity and
which means, that it is possible to have a
rotor, which does not have any deceleration
and
still develops a certain amount of pressure.
But most of the modern compressors, as I have
mentioned, do have deceleration and also
this means, that centrifugal compressors are
indeed affected by flow separation. But not
to the extent, that axial compressor is and
therefore, it is possible to achieve much
higher
pressure ratio per stage from a centrifugal
compressor, as compared to axial
compressors.
Now, that is one set of governing equation
that we have discussed. There is one more
aspect of centrifugal compressor, which is
also true with some of these radial flow
machines. We shall discuss about what that
equation of conservation is and that is also
valid for a centrifugal compressor.
So, this is to do with what is known as rothalpy.
Now, if you, let us say, assume steady, viscous
flow without any heat transfer, then in
radial flow scenario we have this particular
conservation equation, which is also valid
for
these radial flow machines, that is, h 1 plus
C 1 square by 2 minus U 1 C w 1 is equal to
h 2 plus C 2 square by 2 minus U 2 C w, that
is, h plus c square by 2 minus delta u C w.
It is basically conserved parameter in a centrifugal
compressor or even in any other
radial flow machines.
So, this is usually denoted by symbol I and
this is known as the rotational enthalpy or
rothalpy for short. It is called rotational
enthalpy because it combines enthalpy in the
conventional sense, that is, h plus c square
by 2 and the component, which is associated
with the, component which is associated with
U times C w, which is to do with the
tangential velocity and therefore, it has
been observed, that this parameter generally
is
conserved as it, as the flow take place through
an impeller.
And the change in rothalpy in some cases,
one does see that there is a change in, in
rothalpy is primarily because of fluid friction,
which is acting on the stationary shroud.
So, that is, if you consider the impeller
plus the shroud, there could be certain amount
of
losses taking place as the result of the shroud
and that probably, would explain the
amount of loss in rothalpy, which might be
observed in some analysis, but in general,
in
radial flow machines rothalpy is a conserved
quantity. So, in centrifugal compressor also,
in most of the analysis conservation of rothalpy
is assumed to be satisfied as the flow
takes place through the impeller.
So, having understood some of the fundamental
governing equations of a centrifugal
compressor, let us now look at the different
components of a centrifugal compressor and
also, look at how the flow develops as it
passes through these different components.
So,
we will be discussing about 3 distinct components:
one is the impeller, 2nd is the
inducer, which is also a part of the impeller
in fact, and the 3rd is the diffuser, which
is
the other stationary component of the stator
in a centrifugal compressor. So, let us begin
with the impeller, which is the rotor of a
centrifugal compressor and the most crucial
component in a centrifugal component, compressor.
So, impeller is the component, which draws
the working fluid and it is like the rotor
as
we have discussed for an axial compressor.
And impeller has diverging passages, which
diffuses the flow to a lower static pressure
and well, higher static pressure and lower
relative velocities. And that different ways
or different configurations of an impeller,
it
could be either single sided or double sided,
shrouded or un-shrouded and so on. Now, in
impeller, the working fluid, besides deceleration,
it will also experience centripetal
forces because of the rotation itself and
displacement of the rotational, of the fluid
elements. And therefore, besides the fact,
that the fluid decelerates and diffuses, there
is
also a certain amount of centripetal force
acting on the fluid elements as it passes
through
an impeller.
Now, there are 3 different types of impellers
or impeller blades that are possible. Now,
simplest type is the straight radial type
or one might have forward leaning blades or
backward leaning blades. Now, forward leaning
blades are considered to be inherently
unstable and we will see the reason for its
unstability probably in the next class, where
we will be talking about performance analysis
or performance characteristics of
centrifugal compressor. So, we will see the
reason for, why forward leaning blades are
not really used; that is probably something,
which I will be explaining in next class.
The two other configurations, which are commonly
used, are the straight radial blades
and the backward leaning blades. So, both
these configurations are commonly used in
modern day compressors centrifugal compressors;
so, straight, radial backward leaning
and forward leaning blades.
Let us take a look at what these 3 different
blading configurations are. We will start
with
straight radial first. So, this, the one that
is shown in center, is a typical straight
radial
blade, this is the direction of rotation and
this is the velocity triangle of the flow
as it
leaves the impeller. So, V 2 is the relative
velocity leaving impeller, C 2 is the absolute
velocity and U 2 corresponds to the blade
speed at the tip of the impeller.
And so, as you can see, the flow leaves the
blade radially as V 2 is indeed radial, that
is
why it is called straight radial blade. If
you look at the forward leaning blades, V
2 leaves
the blade tangentially, that is why V 2 is
at a certain angle to the impeller vanes at
the
exit and it leaves at an angle of beta 2,
which is negative. So, forward leaning blades
have a negative blade angle of beta and the
velocity triangle is what you see here, C
2
and U 2. Backward leaning blades, on the other
hand, had a positive beta, beta 2. And so
you have beta 2 and so you have U 2 in this
direction, which has a positive blade angle
beta 2 and C 2 is the absolute angle and U
2 is the blade speed at the tip.
So, these are the three different configurations
of impellers, which are possible and two
of them, as I mentioned, straight radial and
backward leaning are the ones, which are
commonly used. Of course, the, the straight
radial blades are, have conventionally been
commonly used because it is simpler to construct
as well as the fact, that the blade
should not have to undergo lot of stress because
as you bend the blades, the stress on the
blades become substantial, but a modern day
design and materials permit us to use these
complicated shapes as well. In fact, some
of the blades have a combination of straight
radial and backward leaning geometry. So,
there are blades, which have a combination
of
backward and straight radial as well.
So, that is about the impeller, where, which
is probably the more crucial component of
a
centrifugal compressor. And we have seen the
velocity triangle corresponding to these 3
different configurations of a centrifugal
compressor impeller.
Now, there is another component, which is
usually part of the impeller itself. We have
already seen that in the pictures I had shown
in the earlier, probably the 3rd slide in
today’s class, where there, the initial
part of the impeller, as you have probably
have
noticed is, is bent. So, there is curvature
given to initial part of the impeller and
that is
known as an inducer. And an inducer is basically
a component, which is just ahead of the
impeller or in; in fact, it is almost, always
initial part of the impeller itself. The basic
function of an inducer is to guide the flow
smoothly into the impeller in the absence
of
an inducer when the impeller is rotating.
There is a relative component at the impeller
inlet and in the absence of the inducer, the
relative velocity enters the impeller at a
certain angle and there could be flow separation
taking place from the impeller (( )). To
avoid that, one uses set of blades, which
are like guide vanes; these are known as
inducers.
So, inducer is the inlet, impeller entrance
section, where the tangential motion of the
fluid is basically changed to the radial direction.
And one may have either the
acceleration or some amount of acceleration
within the inducer, as we will see it later.
Inducer, the basic function of an inducer
is to ensure, that the flow enters the impeller
smoothly; without inducer, the flow operation
is likely to suffer from flow separation and
high levels of noise because of the flow separating
from the impeller.
So, this is schematic of an inducer and there
are two views of the inducer shown. So, the
initial part of the impeller, as you can see,
this part of the impeller is the inducer and
if
you take a cross section of the inducer, one
would see vanes, likes what is shown here.
So, the inlet velocity triangle of an impeller
would look something like this that the flow,
assuming that the flow is coming at an axial,
in an axial direction C 1 and because of the
inducer, the relative velocity is V 1 and
this is at an angle of beta 1.
So, this is the inlet blade’s speed, which
is U 1 and the flow leaving the inducer could
be
a velocity of V 1 prime, let us say at the
tip of the inducer. So, that is why is called
V 1,
denoted by V 1 prime, with a subscript t,
which responds to the tip of the inducer.
Now, if you look at the velocity triangles,
you can see, that since the blade’s speed
changes all the way, hub to the tip, the velocity
triangle and the angles at the hub beta h,
beta mean and beta tip, they are quite different,
that is because of the fact, that the
velocity, the blade speed continuously changes
from the hub to tip. And therefore, if you
take the velocity triangles at the hub, the
mean and the tip, velocity triangles are different
because of the fact, that blade angles are
changing, which means, that there is certain
twist to the inducer itself as it, as we look
at the inducer from the hub and trace it all
the
way to the tip. So, there could be a certain
amount of twist.
Now, from the velocity triangles we have seen,
that the velocity leaving the inducer,
relative velocity leaving the inducer could
be, is denoted by V prime t and therefore,
V
prime t is a component. It is, it is related
to the inlet relative velocity through the
blade
angle. So, V prime t is basically equal to
V 1 t time cos beta 1 t and so you can see,
that
since, V 1 V, V prime t is equal to V 1 t
times cos beta 1 t, there is a certain amount
of
diffusion taking place even in the inducer.
That is because, V 1, V prime will always
be
less than V 1 because V prime t is equal to
V 1 times cos beta 1 and that means, that
there is a certain amount of diffusion also
taking place in the inducer.
And similarly, the Mach number is related
to the inlet Mach number through the blade
angle beta 1. Now, the 3rd component that
we will be discussing is the diffuser. So,
we
have seen the impeller, the inducer and now,
we will talk about the diffuser.
Now, diffuser is, has a function very similar
to that of a stator of an axial compressor,
that is the deceleration, which was taking
place in the impeller continues and that
continues in the diffuser, where the flow
is further decelerated. Of course, there is
neither
energy addition nor, of course there is a
certain amount of pressure loss as I mentioned,
total pressure loss taking place in the diffuser
vanes, but there is static pressure rise
continuously taking place in the diffuser
as well.
So, the flow leaving the impeller is at a
very high speed and so one can convert part
of
that kinetic energy into pressure rise or
static pressure and that is basically through
the
diffuser. And the different types of diffusers,
which have been used in different types of
applications and there are vaned type diffusers
and vaneless type pipe diffusers and
channel diffusers and soon. So, we will discuss
some of these aspects and different types
of diffusers in the next few slides.
So, the high velocity, that is of the flow
leaving the impeller, is basically decelerated
using a diffuser and the diffuser basically
decelerates the flow and thereby, it reduces
the
absolute velocity of the working fluid. And
how much deceleration takes place depends
upon, firstly, the application for which the
compressor is being used, as well as the
efficiency of the diffusion process itself.
And since the diffusion is, as we have discussed
many times before, is a, is a process,
wherein the flow has to encounter an adverse
pressure gradient, the chances of or the risk
of flow separation is always there when the
flow encounters an adverse pressure
gradient. And therefore, the amount of diffusion
that one can achieve in a stationery
component, like a diffuser, will depend upon
how much the flow can withstand the
pressure gradients.
Therefore, the diffuser flow is, is kind of
always affected by or limited by the fact,
that
there could be chances of flow separation
taking place. And so the flow basically leaves
from the impeller in a radial direction and
then, there is a certain space or gap between
the impeller exit and the diffuser beginning,
and that is called the vaneless space.
And actually, the diffuser as we will see
little later, that diffusion continues even
in the
vaneless space and after that, the flow enters
the diffuser or the vaned space and
diffusion continues even further in the vaned
space.
So, the fluid, which leaves the impeller,
it leaves the impeller radially outward and
then
it passes through a vaneless region and subsequently,
through a vaned diffuser. Now,
there are different types of diffusers, as
I mentioned, vaned type diffusers, vaneless
type
diffusers. These are diffusers, which are
conventionally being used and if you look
at
compressors, centrifugal compressor, which
have applications in aero-engines, these
conventional types of diffusers may not release
of the purpose, one need to employ better
diffusion mechanisms of the flow exiting the
impeller.
So, in aero-engine centrifugal compressors,
one might encounter diffusers, which are
known as pipe diffusers or channel diffusers,
which for, which are much more efficient
and more amenable to integration with the
combustion chambers. For example, if you
have can type combustion chambers, then it
is easy for distributing the flow from these
pipe diffusers and directing them towards
these can type of combustors. So, these types
of diffusers, which are used in aero-engines,
are normally not the vane type diffusers,
which are used in other applications; diffusers
used in aero-engines are usually the pipe
type of diffusers.
We will do now a very simple analysis of the
flow through a diffuser. We will restrict
our discussion to diffuser, the vane type
of diffuser because it is much more simpler
in
understanding and analysis and we will restrict
our discussion to these conventional type
of vane diffusers.
So, this is the impeller vane and the flow
exiting the impeller, first enters into a
certain
region, known as the vaneless space and then
it is guided out of the compressor into the
volute through the diffuser vanes.
So, as the flow leaves the impeller, it basically
leaves the impeller with a radial velocity
and this is the radial direction as you can
see. And so, the absolute velocity that actually
leaves the impeller is at an angle of c, absolute
velocity c. And so, as the flow leaves the
impeller and it moves towards the vaned diffuser
because of the velocity triangle, as you
see here, the flow actually follows, what
is known as logarithmic spiral because of
the
fact, that the flow leaves the impeller in
a radial direction and then it suddenly
encounters vaneless space.
So, if you consider an incompressible, let
us for the moment consider an incompressible
flow in the vaneless region, which has constant
axial width. The mass flow through the,
through the vaneless space, let us represent
that by m dot. So, from the continuity
equation we have m dot is equal to rho times
the angular area, that is 2 phi r h, where
h is
the width of the vaneless space times the
radial velocity C r. So, this is equal to
a
constant.
Now, from the conservation of the angular
momentum we also know, that r times C w is
also a constant. Therefore this means that
this ratio C w by c r is also a constant,
that is,
velocity ratio, the tangential velocity to
the radial velocity. As we have seen in the
velocity triangle, this is also equal to a
constant and the angle is given by tan alpha.
So,
here, the angle alpha is basically the angle
between the velocity and the radial direction,
the absolute velocity leaving the impeller
to the radial direction.
So, this means that this velocity is basically
inversely proportional to radius and so as
we
increase the radius, the velocity would kind
of reduce. So, in the vaneless space we have
velocity, which is inversely proportional
to radius and therefore, with increase in
the
radius, the velocity, absolute velocity actually
reduces, which means, that there is a
diffusion taking place even in the vaneless
space. And once the flow leaves the vaneless
space and enters the diffuser vanes, since
the flow is guided through a diffusing passage,
which has an increase in area in the radial
direction, the flow continues to decelerate
and
there is further static pressure rise taking
place even in the vaned section of the diffuser.
So, what we can see here is the fact, that
the vaneless space also contributes to the
diffusion overall diffusion process, which
begins right from the inducer. As we have
seen, that diffusion also takes places in
the inducer vanes, it continuous in the impeller.
Of course, in the impeller there is another
mechanism, which contributes towards the
pressure rise, which is the centripetal forces,
which are coming there.
Once the flow leaves the impeller and enters
the vaneless space, the flow continuous
deceleration and that is because the velocity
is inversely proportional to r and it follows
a
logarithmic spiral. From there, from the vaneless
space, the flows enters the vaned
diffuser space, where the flow is further
decelerated and the flow exiting the diffuser
vanes, then goes into the volute or the collector,
and then it is exhausted from the
centrifugal compressor. So, this is the overall
working of a Centrifugal compressor.
So, what I will do is quickly take a recap
of what we have discussed in today’s class.
We
had discussed about 2 distinct aspects of
centrifugal compressors. We started of our
discussion today with the thermodynamics of
a centrifugal compressor, where we looked
at how diffusion is indeed achieved in a centrifugal
compressor from a thermodynamic
perspective in terms of temperature and entropy.
We have seen, that in a centrifugal compressor
energy is actually added in the impeller,
where, where we have an increase in the stagnation
temperature, which also contributes
to, which also gets converted into the stagnation
pressure rise taking place in the
centrifugal compressor.
After the impeller we have the vaneless space
and the diffuser, where there is no energy
addition taking place, but static pressure
rise continuous to take place through these
components as well.
So, after the temperature entropy diagram,
we also wrote down the governing equations
for centrifugal compressor and how one can
analyze the flow through a centrifugal
compressor. After this we took up the individual
components of a centrifugal compressor
and how one can analyze the flow through these
different components.
We have seen, that impeller, there are different
configurations of an impeller: the straight
radial, the backward face, backward leaning
blade and the forward leaning blade. I made
a passing remark, that forward leaning blades
are unstable. We will discuss details of that
in the next class, where we take up the instabilities,
etcetera in centrifugal compressor.
And then, we discussed about the flow through
an impeller and the velocity triangles at
the inlet of an impeller, as well as the exit,
as the flow exits the impeller, and how the
velocity triangle gets modified as we change
the configuration of the impeller from
straight radial to backward leaning blades.
We then discussed about inducer and the flow
analysis of the, as the flow passes through
the inducer, we have seen, that it undergoes
a deceleration. And as the flow leaves the
impeller, it enters into a vaneless space,
diffusion continues in the vaneless space
as well
as in the diffuser or the vaned space of which
follows the vaneless space. So, this was in
a nutshell about what we had discussed in
the various slides we had for discussion today.
And we will continue with discussion of different
aspects of centrifugal compressors in
the next class as well. We will take up important
aspect of centrifugal compressors, that
is to do with Coriolis acceleration first
and then we will define, what is known as
the slip
factor associated with the centrifugal compressor.
After that, we will take up the performance
characteristics of centrifugal compressors
and we will also talk about details regarding
stall, surge and choking associated with
centrifugal compressors.
So, we will take up these, some of these topics
for detailed discussion in the next class
on
centrifugal compressors. Subsequent to that
of course, we will have one session, which
would be a tutorial on centrifugal compressors.
We will solve some problems, which are
related to centrifugal compressors and we
will also have some exercise problems for
you,
which you can solve based on our discussions.
So, in the next class we will basically have
these topics for discussion. We will talk
about Coriolis acceleration, the slip factor,
the performance characteristics and stall,
surge and choking associated with centrifugal
compressors. So, we will take up these
topics for discussion in the next class, which
would be lecture number 32.
