We are talking about gas turbines; we have
done Axial flow turbines in the last lectures.
Today, we look at the Radial flow turbines.
Now, chronologically the Radial turbines were
indeed actually considered for application
in aircraft gas turbines even before the Axial
flow turbines. The reason is very simple Radial
flow turbines the shape and the configuration
of it is something very simple. As, we will
see in a few minutes, it actually looks a
very similar to a centrifugal compressor.
Now, centrifugal compressor as you actually
appear before the Axial flow compressors,
because they were very simple to configure
and also the very robust machines.
Similarly, Radial flow turbines are very robust
machines and they are very easy to configure.
As a result of that they were indeed considered
for application even before the Axial flow
turbines there is another reason just like
centrifugal compressors, the Radial flow turbines
have very high energy extraction capability
in one single stage. Now, this is attractive
simply because in aircraft gas turbines as
we have discussed before you need to extract
as mass energy per unit mass flow as possible.
So, that the amount of work that is to be
supplied to compressors can be done in minimum
number of stages in the Axial flow turbine
or gas Radial flow turbine used in aircraft
engines.
Now, Radial flow turbines intrinsically has
the capacity to extract a lot of work, whereas
in Axial flow turbines that intrinsic capability
was lacking to begin with and of course, now-a-days
Axial flow turbines as we have seen can have
very high energy extraction capability because
of the high temperature input into the Axial
turbines. Now Radial flow turbines, we will
see even without high temperature input high
energy gas it can still extract a lot of energy
output or unit mass flow because of its intrinsic
way the way it performs and the way it is
configured. As a result it is a very attractive
proposition even today for various gas turbine
applications and we will see as we go along
that there are certain areas in which Radial
flow turbines are indeed, extremely useful
and indeed the more preferred form of energy
extraction than even compared to Axial flow
turbines, especially in small engines.
We shall see that Radial flow turbines has
another advantage or one may call it restriction,
whichever way one wants to look at it: the
Radial flow turbine rotor does not use aero
foil sections, now Axial flow turbines use
aero foil sections. As a result of which it
its shaping is needs to be a very intricate
for reproduction of those aero foils sections
very accurately whereas, Radial flow turbine
does not use any aero foil sections. As a
result of which the rotor of Radial flow turbine
has a shape as I said very similar to a centrifugal
compressor and it uses the 3D shape for energy
extraction and this 3D shape of course, is
something which is become of great interest
in the modern research. Again, as I mention
the Radial turbine actually appeared before
the Axial turbines, but for a long time they
were not considered and most of the development
indeed to place with Axial flow turbines.
Recently lot of people have taken a fresh
interest in Radial turbines and have tried
to give it more and more accurate shapes;
3D shapes and more and more new designs, which
renders it is use to various kinds of applications
in a modern small gas turbine segments. So,
these are various advantages and one can say
some restrictions of the use Radial flow turbines.
Let us take a look at some of these Radial
flow turbine configurations.
The Radial turbines that one uses can also
be considered as some kind of mix flow turbines,
if one compares that with, let us say Axial
flow turbines there is a chance that. You
may like to look at how the flow is actually
executing its path to the turbines. Now, through
the turbines are Axial flow turbine as we
have discussed the flow essentially keeps
its path along the line parallel to the axis
in Radial flow turbine it quite often takes
a path partly to begin with parallel to the
axis and then goes out radially and that is
why is often called Radial flow turbine.
Now, as I mention it looks very similar to
a centrifugal compressor. As result of, which
it is able to extract lot of work, just like
centrifugal compressor in one single stage.
That makes it very attractive for use in small
aircraft engines, which means you can have
the combination of a centrifugal compressor
and a Radial flow turbine and this creates
a very compact energy creator for gas turbine
engines for aircraft usage. As one see in
these diagram, this Radial inflow turbine
centrifugal is typically out flow compressor
and the flow comes in from the outer segment
of the turbine through this volute shaped
rotor this is the rotating element or impeller.
Then goes out through the impeller of a executing
a rather complicated shape through this veins;
this rotating veins and this passage through
this veins is what transfers the energy from
high energy gas to the rotor. So, transfer
change of momentum in the lateral or rotating
direction, what actually executes the transfer
and the work transfer. Now, this how the work
is transferred we will of course, have a look
at this in some detail in a few minutes from
now. Now, because of the fact that we have
a shape here, we is as I mentioned not of
aero foil shape and as you can see here the
edge of these rotor is likely to be rather
thin and not round head like an aero foil.
The result is that it is generally considered
not feasible; not employee cooling technology.
As, we have done in Axial flow turbines in
the Radial inflow turbines. There is no space
for employing or deploying cooling technology
here.
However, lot of research is going on these
days to somehow employee cooling technology
here. So, that the temperature of the Radial
inflow turbines can also be increased in a
manner, such that they can actually use high
temperature gas from combustion chambers somewhat
similar to that of Axial flow turbines. So,
some of those things have now gone into research
and it is hope that some of it will actually
be used in future for Radial inflow turbine
designs.
If you take a digital model of a Radial inflow
turbine, it is seen that if you have the blades
over here as one seen the flow coming through
these blades indeed go through a passage.
That is actually an expending passage and
a result of which the flow comes in through
the rotor over here. Then as you can see the
passage here is essentially converging passage
and then the converging passage takes a curve
linear converging passage. So, this straight
converging then gives into curve linear passage
and then the flow indeed goes out actually.
So, in Radial inflow turbine there is every
possibility that flow will come in radically
and go out actually. This is one of the reasons;
why some people may like to call it a mix
flow kind of a turbine, because part of the
exit flow is indeed again actual.
Now, this something which people would you
knows like to look into in more and more modern
designs. One can see a digital model of such
a Radial flow turbine over here. On the right
inside you can see top view of modern Radial
flow turbine, in which one can see that the
flow is coming in and it is getting into converging
passage and then a part of the rotor over
here actually is overlapping the outer parts
or the inner and outer parts are overlapping.
One can see the number of veins in the inner
part indeed different. As a result, the flow
which is coming from the outer ring or outer
rotor, let us say gets often spilt up in two
passages and this flow then gets split up
in two passage: one coming into this passage;
another going into that passage.
As a result of which you have further convergence
through the inner part of the rotor and this
is one kind of a modern design that people
have been trying to develop to extract more
work from Radial inflow turbine. As, I mentioned
Radial inflow turbines have intrinsically
more work extraction capability and this is
one way of trying to increase the Radial turbine
a work extraction capability in some of the
modern designs.
Now, let us take a look at: something of fundamental
issues related to Radial turbine. Typically
in a Radial turbine, you have a some kind
of a collector or scroll whatever, one may
like to call it, where flow is coming in.
Let us say from the combustion chamber, which
are hot gas high pressure gas; high potential
gas and then this high potential energy gas
is released through the static which is of
nozzle stator, which is of nozzle shapes and
these are blades. It is possible that these
could be made of air fall sections. So, the
stator blades or stator nozzle blades could
indeed be aero fall section blades. Now the
flow here, coming in actually in subjected
to again converged passage between the two
blades.
So, the passage here is converging and that
creates the nozzle effect and then this nozzle
effect creates the high velocity exit jet
C 2. So, this coming in with small velocity
may be small c 1 and it is going out from
these nozzles with the very high velocity
C 2 and then this c 2 is transform to V 2
which could be Radial going into to this Radial
turbine rotor.
So, quite often especially in aircraft gas
turbine even to this day the relative velocity
V 2 that goes into the rotor could actually
be Radial and quite often may be called C
r 2 or V r 2 signifying that it is essentially
a Radial flow going in the relative frame
of the rotor itself. This flow goes through
the rotor and as I was mentioning it takes
almost a 90 degree turn through this rotor
if one looks at this side diagram cutout diagram
and comes out more or less actually.
So, when it comes out from the rotor over
here it comes out more or less actually and
it comes out with a velocity V 3.Now, it goes
in with the velocity V 2 over here into the
rotor and then it takes a large turn. Then
comes out with the velocity V 3 and in a craft
gas turbine as we shall see we will see probably
that V 3 is likely to be significantly more
than V 2, which means there is a clear increase
of velocity r acceleration through this rotor.
This kind of as we have seen in case of Axial
flow turbines or essentially refers to as
reaction turbines. So, aircraft Radial turbines
indeed are often or most of the time reaction
turbines, which means there is increase of
velocity from V 2 to V3. Now, V 2 was essentially
a Radial and hence we could call it C r 2
or V r 2. On the other hand V 3 is a neither
Radial nor actual it comes out at an angle.
If you look at the plane over here, it comes
out at this angle which is kind of parallel
to rotor curvature that is given to the exit
side of the rotor veins and then of course,
it creates this vector diagram in which the
rotational speed of the rotor at that station
gets added up and when added up V 3 and U
2. You may probably get an exit velocity C
3 which could indeed be actual. As result
of this the flow is coming in radially. It
is going out in absolute frame actually. So,
the Radial inflow is relative at the actual
output is indeed absolute. So, this velocity
could possibly be going out actually. So,
this is a kind of intended Radial inflow turbine
that could be typically used in aircraft gas
turbines.
As a result of that the flow comes out here,
actually at let us say station three and quite
often after station three there is little
bit of a diffusion of flow to station4. Now
this allows the pressure, the static pressure
to go up a little to a certain comfortable
static pressure for a delivery to somewhere
else may be to the exhaust system; this allows
the pressure at the station 3 to be very low.
Now, if you allow the station three pressures
or static pressure more correctly to go rather
low you would indeed be allowing the turbine
rotor to operate under higher static pressure
ratio. If you do that the work extraction
capability of the rotor indeed goes up. So,
this is a small bit of trick, which the aerodynamic
designer often employee that you put a small
diffuser over here. The exhaust of the diffuser
matches the pressure that is required for
the exhaust system, which may indeed ambient
pressure where as the pressure at station
3 is actually lower.
This gives high pressure ratio across the
rotor from two to three and this high pressure
ratio as we know and as we shall see in a
few minutes. Actually, allows more work extraction
capability across the rotor. So, this is the
kind of general fundamental principal based
on which the Radial inflow turbines actually
operate indeed. It is possible that the entry
to the rotor, which we have shown here as
essentially Radial V r 2 may not be exactly
Radial it may be at some angle and the exhaust
from the rotor may not be exactly actual it
may indeed at small angle to that at actual
direction. So, that may happen, but most of
the aircraft gas turbines quite often stick
to this principle because it is simple.
It also allows us; we shall see it allows
maximization of the work extraction. So, maximization
of the work extraction, typically in aircraft
engines is very important because this allows
you to supply more work to the compressor
and do more compression work. So, this is
the fundamental method by which a typical
Radial inflow turbine works.
Let us take a look at a simple thermodynamic
basis on which this Radial inflow turbine
as to work, because as we have discussed before
every component in the gas turbine engine
has to confirm to the thermodynamic matrix
on which this whole engine is working. So,
let us take a quick look at basis Radial inflow
turbine on its thermodynamics. Now, it starts
from a station 0 1 from which the flow is
indeed accelerated and it accelerates to 0
2. Now, we do in 0 1 and 0 2 there is no work
extraction if there is only a change of velocity
from C 1 to C 2 and it comes out with a high
kinetic energy head. Now, this is what was
intended for all turbine work that why very
high kinetic energy head impinges on the rotor
for work extraction propose. So, it creates
this high kinetic energy and then of course,
it enters the rotor with a velocity V 2 which
is what I shown here and typically V 2 would
indeed be much lower than C 2.
We shall that C 2 could indeed be a pretty
close to sonic velocity it could be equal
to mach one over there where as V 2 is like
here to be much lower than that and then of
course, it could possibly accelerate from
V 2 to V 3 which is much higher and V 3 could
be pretty close to sonic, but by design most
people to avoid going sonic because in a rotor
if you shafts it could create more losses
and bring down. The aerodynamic efficiency
of the blades hence quite often V 3 may not
actually goes sonic and then finally, it goes
out with the velocity V 3 at the exit station
0 3, now between 0 2 and 0 3 the work has
been extracted.
So, the enthalpy h has come down from 0 2
to 0 3 because of the work extraction. That
has happen it has come down from pressure
line P 0 2 to P 0 3, it has come down from
temperature t 0 2 to t 0 3 and all these downward
parameters simply signify the work that is
been given up two the rotor in form mechanical
work. Now, what happens is at the station
three as we have just seen quite often a small
bit of diffusion is employed and this diffusion
takes it from 0 3 to 0 4. This travel from
0 3 to 0 4 may involve a small loss of pressure
from P 0 3 to P 0 4 no work is done is there
and during this process the velocity may come
down from C 3 to C 4.
This is what is intended that it goes out
with a lower velocity and a higher static
pressure P 4, which you can see here is a
much higher than the static pressure P 0 3
and this is what is intended. So, this is
how the thermodynamics of a Radial inflow
turbine actually works. There are couple of
other things, which we shall come back to
this diagram what is this enthalpy we shall
come back to that and the fact that U 2 square
could possibly be higher than is indeed higher
than U 3 square and what it means and will
come back to this that those parameters in
a few minutes. just one simple thing that,
if you have a purely Isentropic turbine that
flow comes out from 0 1 goes all the way down
to 0 3 double prime and then 0 4 double prime.
It is a vertical drop all the way and that
signifies Isentropic turbine performance.
That is of course, as we know the Ideal performance
based on which real performance is often configured
and hence the efficiencies are cost against
this Ideal performances and efficiencies are
indeed call high Isentropic efficiencies.
we will come back to couple of these parameters
in a few minutes.
Now, if you look at the way it works, typically
the tip of the rotor the veins are usually
Radial and straight and there after it takes
a 3D curvature, as we have just seen which
guides a flow from Radial to actual. In the
process also does a lot of acceleration and
it accelerates the flow to a lower Radial
station and it finally, let it out at an angle
beta 3 with a velocity V 3. Now, lower Radial
station indeed creates the lower velocity
U 3 square. So, the gas velocity along with
rotor velocity in the tangential direction
comes down from U 2 square to U 3 square.
So, the exit gas tangential velocity component
is much lower than the entry at the tip. This
is one of important issues related to Radial
turbine, which is quite different from actual
turbine. In a typical actual turbine U 2 would
have been equal to U 3 the entry and exit.
Hence, there would have been very little differential
available there here we see that there is
a large differential available between U 2
and U 3 and in terms of energy half U 2 square
and half U 3 square the difference is indeed
quite large. The flow goes out with their
absolute velocity C 3, which most of the time
are quite often by design is made actual.
So, it becomes c a 3 and then this is actually
diffuse to a lower exit velocity C 4. So,
the C 1 square is what it comes in with and
C 3 square is what it goes out with and finally,
it exited a small velocity C 4. So, this how
the thermodynamics of the Radial flow turbine
may be cost.
Now, let us take a look at some of the parameters
that we would like to discuss at the beginning
of the gas flow. It starts with a velocity
C 1 goes on to velocity C 2 which I mention
is indeed quite high in the ring nozzle or
stator nozzle and this creates the high velocity
jet that impinges on the rotor. Now, total
enthalpy change across these nozzle is constant
no work is being done. So, the total enthalpy
remains constant and the static enthalpy change
is shown here, in terms of the change in the
velocity form C 1 to C 2 now this is a larger
change and hence there is large change in
the static enthalpy that can be quantitatively
written down.
Now, if you go across in an Ideal flow then
there is no loss of pressure, but we have
just see that the indeed would be a loss of
pressure from P 0 1 to P 0 2. Now, what happens
is this difference between Ideal flow and
real flow means that there would be a difference
in the velocity C 2 that is finally, achieved
at the end of the stator nozzle. The real
velocity C 2, the Ideal velocity could be
C 2 prime and it stands to reason that Ideal
velocity would have been higher than the real
velocity C 2 and this difference between the
two or the ratio of the ratio of the two is
an important issue of the performance of stator
nozzle, how much is the difference between
Ideal flow through the stator and the real
flow across the stator.
The losses suffered by them needs to be them
quantified in actual terms. at the rotor entry
the relative total enthalpy is defined in
terms of h 0 2 to relative and it is equal
to h 2 plus half row V 2 square. Now, this
is of course, different from h 0 2 this is
relative enthalpy that we are talking about
and h 0 2 was absolute enthalpy. Now, at the
station 2 the total absolute enthalpy is indeed
h 0 2 is equal 2, h 2 plus C 2 square.
Now, this actually means that the work extraction
capability is can be now written down in terms
of W by m dot and that is the enthalpy change
across the rotor total enthalpy change across
the rotor from h 0 2 to 3 and this could be
written down as change of a angular momentum
from station 2 to station 3 and this is something
we have done before with earlier compressors
and turbines and that particular theory is
still valid and change tangential momentum
is indeed equal to specific work and that
is U 2 into C W 2 minus u into C W 3. This
differential is what gives us the work extraction
capability of the turbine. So, C W 2 and C
W 3 are the Radial components of the absolute
velocity C 2 and C 3.
This what we had seen in the diagrams earlier
that if you take the tangential component
of C 2 this is what indeed it will come to
be equal to U 2.Whereas a few take tangential
component of C 3 it will come out to be zero
from this diagram. So, the kind of Radial
turbine that are normally used.
we see that C 2 C W 2 comes out to be equal
to U 2 and C W 3 comes out to be equal to
0 and as a result of which the total work
that is possible to be extracted from a typical
Radial turbine is simply equal to U 2 square
and this represents the maximum work that
the Radial turbine can do. So, this is the
kind of work that people would like to extract
from a Radial turbine.
We shall see that the work extraction capability
h 0 2 3 is indeed written down in static enthalpy
change and the kinetic energy change across
the rotor from station 2 to station 3.So,
the differential between the two states of
enthalpy written down as h 0 2 3. Now, this
can one also be written down now in terms
of all the velocity components. So, this comes
out to be U 2 square, minus U 3 square, minus
V 2 square, minus V 3 square, plus C 2 square
minus C 3 square now take a good look at this
equation in terms of all the velocity components;
if we look at the first term U 2 square minus
U 3 square. We see that in Radial flow turbine
there is a clear difference between these
two terms. So, the this term is going to be
positive and its going to be quite large depending
on the size of the Radial turbine and depending
on the rotational speed of the Radial turbine.
So, you because as you know is omega r, omega
is the angular velocity and. So, higher is
the r difference of radius between station
2 and station 3 higher would be the difference
between U 2 and U 3 on the other hand if omega
very large even if r is not very large again
the different between U 2 and U 3 is going
to be quite large. As a result of, which in
a typical Radial turbine, this term; the first
term is going to be contribute significantly
to the work extraction capability of Radial
turbine now if you remember in actual turbine
U 2 was indeed equal to U 3. Hence, this first
term had no contribution to make in Axial
flow turbine sand this is the difference that
Radial turbine as intrinsic capability to
extract more work, because of this first term,
which shows up here.
The second term is indeed V 2 square minus
V 3 square now, if we have a situation where
V 2 is equal V 3 then this term is going zero
which means the rotor is essentially more
or less some kind an impulse turbine; however,
if V 3 is more than V 3 we see that this term
would become additive it will become positive
and hence it would add to the work done capability
of the Radial turbine and in an aircraft gas
turbine most of the rotors indeed reaction
turbines and this then became a positive addition
to the work extraction capability of the Radial
turbine. The third term is different between
C 2 and C 3 this could be very small.
Or it could be some positive value it depends
on the designer he would rather like to make
it such that C 2 at least equal to C 3 or
slightly more than C 3 and as a result of
which one can get a positive contribution
and settle not negative contribution quite
often small positive contribution is extracted
from third term also. So, in a typical Radial
turbine all the three velocity components
indeed contribute to the work extraction capability
and this is what makes a Radial turbine a
better work extractor intrinsically than let
us say an actual turbine working under same
operating conditions.
If we look at this equation, this work extraction
capability specific work extraction all over
again; it depends on the size and the rotor
r pm and as I was saying the different between
U 2 and U 3 can be manipulated during their
time of design to ensure that you have maximum
work extraction from the first term itself
; the second term is a question of how much
reaction you can render through the rotor
and this reaction capability also has to be
built into the rotor shape design; the vein
shape design and then this vein shape will
ensure that you have V 3 which is higher than
V 2 and the third term again by design could
be made such that a small contribution is
main to the work done. So, this is how the
work done capability of a Radial turbine can
be built into it by design.
Now, we have seen that in Axial flow turbine
this total enthalpy term of the first term
is quite often constant and incase of Radial
flow or Radial inflow machines, because of
the significant change in radius the total
parameters quite often in need to modified.
now in case of an Axial flow, turbines what
we would normally assume is that T 0 2 relative
T 0 2 is equal to T 0 3 and P 0 2 relative
would be more or less equal to P 0 3 relative
and we would assume that h 0 2 relative would
be equal to h 0 3 across an Axial flow turbine
incase of Radial flow turbine you cannot do
that because the station from 2 to 3 has as
large change in radius.
this means that you need to create a new parameter
and this parameter is refer to as Rothalpy
or a short form of rotational enthalpy which
is introduced to the Radial flow turbine performance
usages and it is simply defined as Ro 0 2
3 that is across the rotor and h 2 plus V
2 square by 2 minus U 2 square by 2 and this
would be considered as equal to h 3 plus V
3 square by 2 minus U 3 square by 2. So, combination
of the static enthalpy the relative velocity
and then the tangential or rotational energy
component at the two stations at station two
and station three if all of them are put together
then get a term which is called Rothalpy.
And that is a terminology or Rothalpy which
is expected to ideally remain constant across
the rotor and this term then allows you to
compute parameters across the rotor because
that is a constancy that is useful in terms
of computation of parameters from station
2 to station 3. So, Rothalpy is a very useful
parameter while computing the performance
of rotors of a Radial flow turbine.
So, if you look at the whole thing the static
enthalpy change can be written down in terms
of the relative velocity change and the rotor
speed changes, which is at the movement as
the gas speed and if write all that down this
is what you get across the rotor at the exit
duct as I mentioned quite often there is a
small exit duct.
This exit duct is actually not doing any work,
hence the enthalpy; total enthalpy across
this is constant and the static enthalpy change
shows up in the form of change in velocity,
which is what is indented and the C 3 is normally
higher then C 4 it diffuses from C 3 to C
4. So, this exhaust duct is quite often a
diffusing duct that is the only diffusion
that is taking place in this Radial turbine.
If we now look at: the other parameters that
we would like to quantify for Radial flow
turbines these are losses and correspondingly
the efficiencies that come out and we will
look at losses and the efficiencies now if
we look at the nozzle or stator nozzle enthalpy
loss coefficient across this ring nozzle that
we had called ring nozzle.
The zeta nozzle or zeta N can be defined in
terms of loss of enthalpy as I mentioned the
Ideal flow is often give in terms of h 2 prime
and h 2 of course, is a real amount and differential
of the two can be considered to be the loss
and this when normalize by half C 2 square
indeed gives the loss coefficient now this
loss coefficient is what we would like to
quantify or no now one way of a numerically
configuring this loss coefficient is nozzle
exit velocity coefficient which we had defined
described earlier and we can define a parameter
pi n here which is C 2 by C 2 prime. Now,
C 2 prime is the Ideal exit velocity from
the stator nozzle.
C 2 is a real exit velocity and as one can
expect the real velocity would be indeed a
little lower than C 2 prime. Ideally as I
mentioned the flow they are in a typical aircraft
gas turbine would like to go sonic. So, if
the real velocity is sonic, the Ideal would
be slightly less than sonic. So, if this is
Mach one this would Mach 0.96 and 0.97 or
their about and this differential can be written
down in terms of the nozzle loss coefficient,
if we use a conversion of energy of the static
enthalpy. It can be written down that zeta
N is simply equal to one divided by pi N square
minus 1 and these gives us a handy simple
good first cart idea about what could be possibly
the nozzle enthalpy loss coefficient. So,
this is as good starting value for the designers
to understand what the nozzle loss could possibly
be.
Now, similarly we could have a look at the
rotor loss coefficient and connected to the
rotor exit coefficient in terms of the actual
velocity V 3 as oppose to the Ideal velocity
V 3 prime and the ratio of the two is referred
to as pi R and then this pi R can be used
to write down the rotor loss coefficient zeta
R in terms of one by pi R square minus 1.
Now, in many of the normal Radial turbine
designs these values are normally of this
order, if it is subsonic its of the order
of point nine seven; if it is sonic its of
the order of 0.95 and if it is supersonic;
if the flow indeed goes supersonic one could
go down to about to point nine for rotors
this value is quite often of the order of
85 as there are all kinds of losses in the
rotor due to the rotation of the rotor veins
and hence this parameter is likely to be somewhat
on the load side compare to that in case of
stator nozzles.
If, we put together all of them in terms of
how they vary the losses shown here, in terms
of the total enthalpy parameters with reference
to the Ideal value, one can see that you have
at the top losses related to the stator and
then you have the losses that have related
to the rotor vein passage. Now, these are
of course, purely aerodynamic losses mostly
connected to the friction of the flow on the
surfaces of the blades and veins. Then you
have this dotted area, which is the rotor
tip clear encloses when the rotor rotates
you have to leave a small tip clearance.
The flow of a move from one side to another
and tip clearance of an entail set amount
of small loss. You have done that in case
of Axial flow compressors and exactly saying
concept applies here and then there is a small
bit of loss over there and then the rotor
clearance flow creates a winding or rubbing
loss. That is the another kind of loss that
appears over here and then of course, you
have the loss which is related simply to the
turbine exhaust the flow goes out of the turbine
with a certain amount of energy. You cannot
use that any more once it is gone out are
you cannot hardness it any more for work extraction.
Now, that amount goes up as the specific speed
of the turbine goes up the specific speed
is defined here it is a non-dimensional parameter
and this non-dimensional parameter is often
useful in characterizing theses turbine performances.
That is what I shown over here and as the
speed goes up; more and more exhaust energy
goes out on used and we have to find some
other way of using it either through a nozzle
of a jet engine or some other usage and hence
the losses connected to the exhaust goes up
tremendously. As a result of which one can
see that total amount of losses indeed are
increasing. So, these are various loss parameters
that one sees in a Radial flow turbine and
each of these components would have to be
looked into by the designer to ensure that
the turbine finally, as a reasonable efficiency
parameter during its operation. We can looked
at the efficiency definitions.
Now, that would need be created by that turbine
designer then we have to two different efficiencies
one is referred to simply as a total to total
efficiency which takes the parameter from
0 1 to 0 3 total parameters as compared to
0 1 two 0 3 prime, which is the Isentropic
parameter across the enthalpy entropic diagram
that we have done before. This numerator denominator
comparison gives us what is known us total
to total efficiency parameter. The other efficiency
definition is the total to static efficiency
definition and that is often simply given
as eta T S for turbines and this is again
the work done; the total work done as oppose
to h 0 1 minus h 3 double prime as oppose
to h 0 1double prime which means the denominator
now takes it from h 0 1 two h 3 double prime.
Let us quickly go back to the h s diagram
once more, now if see here the flow ideally
or Isentropically drops all the way from h
0 1 to h 3 double prime. That is a vertical
drops straight from h 0 1 to h 3 double prime,
on the other hand h 0 3 double prime is somewhere
over here, which contains the kinetic energy
of the exhaust flow. So, typically h 0 1 minus
h 0 3 double prime would be much lower than
h 0 1 to h 3 double prime and hence we have
two different denominators: one for total
efficiency; another for total to static efficiency.
So, let us go back those efficiency definitions
and we can see now that intrinsically the
total to total efficiency numerical value
will always be higher than the total to static
efficiency numerical value. Hence, both of
them are useful typically in aircraft gas
turbine in a jet engine the total to total
efficiency is often used, because the exhaust
gas would being used further through the jet
engine nozzle; whereas in a land based application
or in applications; where the aircraft engine
has no jet thrust creating capability the
efficiency of the turbines that should be
used to signify its utility or indeed efficiency
is the total to static efficiency, because
by design then the total to static efficiency
needs to be maximized.
Where as in a jet engine, which creates jet
thrust total to total efficiency needs to
be maximized. So, where these turbines are
going to be used is important consideration
in the design of the turbines. Accordingly,
either the total to static efficiency or the
total to total efficiency would need to be
maximized by design. This is what is stated
here that we need to consider the two efficiency
is depending on where the turbine is indeed
going to be used.
We take a quick look at a very modern usage
of Radial turbine which is in micro gas turbines;
the Radial turbines are indeed being very
seriously considered for small mini and micro
gas turbine engines for various kinds of usages.
The small gas turbines may be used in small
aircraft; the mini gas turbines may be used
for various kinds of one mind aerial vehicles,
on mind aircraft vehicles and micro gas turbines
going used for various kinds of power generations,
which are portable power generating units.
We see here a micro gas turbine, which is
credited to the development of which credited
to MIT in US. It simply shows how Radial turbines
have been put together with centrifugal compressors
to create a very small micro gas turbine.
As you can see here, the dimension of this
the diameter which is only 21 millimeters,
the thickness of entire gas turbine is only
3.7 millimeters and how is within that you
have combustion chamber you have the compressor
and this is rather flow comes in through the
inlet it goes through the compressor. It gets
supplied into the combustion chamber. Then
you have the turbine over here: the red part
is the turbine flow and it goes out through
the exhaust at the it comes out from the top.
Let us comes in from the top and let us say
goes out from the other side which is red
flow the turbine here is shown. You have the
ring blades, which are the stator nozzles
and the inner ones or the designed rotational
once, which create the work or the energy
that is extracted from fluid to run the compressor.
So, this is how typically micro gas turbine
is expected to perform and these micro gas
turbines are mentioned are portable units.
They can be as small as indeed the button
of this jacket and that is how small they
can be and they create power in terms of quite
a few volts in terms of five tens fifteen
volts. That can actually replace a battery.
So, typical Radial flow turbines as found
all kinds of usages these days and these usages
indeed start from small aircraft engines to
on mind aerial vehicles and then to portable
generating units. So, Radial turbines have
new lives of life in the last five ten years
and all kinds of new designs are coming up
connected to usage of Radial flow turbines
in the next class we will take a look at all
the theories that we have done for actual
turbines and all the theories we have done
for Radial turbines will put together all
these theories to first solve a few problems
connected to actual turbines and Radial turbines.
Then I will leave you with a few problems
to solve on your own using the simple theory
that we have done in the last few lectures.
So, the next class will be some kind of we
will have a tutorial in which I will first
bring you some solved problems and then I
will leave you with some unsolved problems
for you to solve to all by yourselves that
would be in the next class.
