We are talking about radial flow turbines.
And, in today’s lecture, we will be looking
at some of
the issues related to the overall characteristics
of radial flow turbine, and how, one goes
about
designing a radial flow turbine. Now, radial
flow turbines, as you have done in the last
few lectures and we have solved some problems
also. It has given you an idea that radial
flow turbine is a robust machine like centrifugal
compressor, but it has a few limitations
of its own.
And, one of the things is that, its ability
to produce work is not substantially more
than
axial flow turbine, as it was; for example,
in case of centrifugal compressor, which had
an ability to produce work per unit mass flow
is substantially more than axial flow
compressors. So, the difference between radial
flow turbine and axial flow turbine is not
as much as, it was between axial flow turbine
and centrifugal compressor.
Now, radial flow turbine as you have seen
is somewhat, you know, it look like and its
flow is inverse that of a centrifugal flow
compressor. And, in some books indeed, it
is
also referred to as centrifugal turbine. But,
most people prefer to call it radial turbine.
And, the one that we are looking at very closely
is radial inflow turbine because there
have been few radial outflow turbines that
have been designed and have been worked
really speaking. But, radial inflow turbine
is, as been done in the last lectures is a
substantially superior machine, it has ability
to produce more work per unit mass flow.
And, of course it lends itself to very high
temperature and very fast motion or movement
of flow of gas through the machine, as it
is normally done in gas turbine engines that
are
used in land based or aeronautical applications.
So, many of these issues put together for
most practical applications; both aeronautical
as well as non-aeronautical. The radial
flow in flow turbine is the more preferred
form of machine.
Now, we will look at some of the characteristic
features of this radial inflow turbine.
And, those characteristic features will also
leads us towards how one goes about
designing a radial inflow turbine, and what
are the primary design considerations that
govern the design of a radial inflow turbine
right from the beginning, right from scratch,
where you have really nothing. And then, we
will indicate that under certain
circumstances when a design is first cut,
good design has been made. One can go to CFD
to get a fine tuning of the design.
So, let us first take a look at what is a
radial flow turbine, which you have done in
the
last few lectures and then from there, we
will look at the basic characteristics of
radial
flow turbine. So, in today’s class we are
doing radial flow turbines, its overall
characteristics, and how that leads us towards
its design features.
Now, let us take a quick look at what you
have done already in the last couple of
lectures. The h-s diagram, you may have done
t-s diagram, but it quickly captures all the
things that are happening inside. The flow
is coming in at 0 1 and then going through
the
nozzle from 01 to 02 and then it produces
work, which brings the enthalpy each down
from 02 to 03. And then, of course you may
have a small bit of diffusion from 0 3 to
0 4
essentially, aerodynamic method to conserve
and make use of the available energy level.
So, at the exit, the flow from the rotor is
going out with a velocity C 3 squared. And,
this
is something, which one has to decide because
the incoming energy into the rotor is C 2
or half C 2 square, is the energy level from
which it comes down to of C3 square. And,
this drop in kinetic energy level accompanied
with this drop in overall total enthalpy
from 0 2 to 0 3 signifies the amount of work
that is produced by the radial flow inflow
turbine. And, of course this graph here shows
the real flow as you have done before. The
straight graph of course, signifies the isentropic
flow as it would have been if the entire
process was totally isentropic.
So, all the parameters that you have done
are sort of captured over here. And, one can
probably relate to the some of the things
that you have done in the earlier lectures.
And,
the flow, the radial turbine actually moves
with a speed of U 2 at the tip of impeller
and
U 3 at the exit face of the impeller.
So, these are the parameters, which we would
have to deal with during the design
process and that is why, we are having a quick
recap of what has already being done in
the earlier lectures.
Now, this is of course, the picture that you
are familiar with; that the flow comes in
from
the tip over here. So, first we have a stator
nozzle, and then through the stator nozzle,
flow gets accelerated hugely and is fed into
this rotor, which has a shape like this; and
that is why, it is called a radial inflow
turbine. So, the flow comes in radially and
then of
course, exits axially or more or less axially
and gets fed into quite often a small diffuser.
So, the flow has been accelerating all the
way. And, after it has left the machine, quite
often a small bit of diffusion is done, essentially
to ensure that the pressure at the end of
the diffuser meets the destination pressure.
And, if that is a little on the higher sides
it
allows the pressure at 3 to be lower. If the
pressure at 3 is lower than the pressure drop
between 2 to 3, can be a little more. So,
this little more pressure drop allows more
work
to be done. So, allowing a diffuser to be
stationed here or placed here, allows P 3
to go
lower and that allows the turbine to do a
little more work.
Now, this is what, has been done in the earlier
lectures. These are, of course velocity
diagrams. This is at the entry to impeller
and this is at the exit of the impeller. So,
you
have to create this jet C 2 through this stator
nozzle. Stator nozzle is essentially
positioned there, to create this jet and then
of course, it comes out with an angle with
a
relative velocity V 3 and absolute velocity
axial. So, it is sort of coming in radially
in
terms of axial velocity and then going out
actually again in terms of absolute velocity.
So, some of these things are normally used
in most radial turbine design. This is kind
of
an ideal velocity diagram. And, this is ideal
velocity diagram at the exit. The real thing
could be a little different. And, of course
in off-design, they would be different. But,
this
is what normally most people are doing in
terms of radial inflow turbines.
Now, let us take a look at some of the issues
that are involved, when you move towards
characterizing the radial inflow turbine and
its design. Now, this particular up lot for
example, tries to capture what are the losses
in a radial turbine and its various
components.
Now you see, ideally as we have seen in the
h-s diagram if the flow is isentropic, then
you know there are sort of no losses. So,
you know this efficiency ratio that we see
over
here, is the work done difference between
ideal and real that is been captured over
here.
And, this actually gives a flat characteristic.
And then, of course we have the losses. Now
the first loss, of course is the stator. And,
that in the stator, you can see the loss actually
increases with the specific speed, which is
a dimensional; a specific speed that has been
defined essentially for all kinds of Turbomachinery.
And, this of course, reduces with the
increase of specific speed. So, let us say
that if you increase the speed, the stator
losses
actually come down. On the other hand, the
next shaded area is a rotor loss in the
rotating vane passages and that also comes
down with the increase of the speed or
specific speed as it is plotted here.
Now, this is because once the speed is increased
in both the places, the local Reynolds
number actually goes up. And, when the Reynolds
number goes up, the boundary layer
growth actually is reduced substantially as
the flow in turbine is accelerating flow.
And,
when you have a higher Reynolds number, the
boundary layer is substantially reduced
and hence you have a reduction, essentially
in the losses due to reduction in the boundary
layer growth. Towards the end, towards a very
high specific speed the losses again go up
because of the friction losses that go up
with very high specific speeds.
So, this slight increase is mainly due to
the high speed of the flow, which results
in
higher friction losses. Then, we have the
rotor tip clearance losses. As you know the
impeller positioning of the impeller leaves
a little clearance at the tip of the impeller
between the stator nozzle and the impeller.
And, this of course, has a loss penalty that
has to be bounded by the machine and comes
out in the process of efficiency; however,
as you can see the tip losses also go down
with the specific speed and it becomes very
low at high speeds.
The next is the rotor clearance flow, due
to the rubbing of the losses. As the rotor
is
rotating, the flow that is captured between
the rotor and the stator, and the rotor and
the
body outside the impeller, that is, the shroud,
and the back plate; that fluid is captured
over there and is continuously being rubbed.
It is actually being carried by the impeller.
On the other hand, one surface of it is sticking
to the shroud body or the shroud surface.
So, as a result of this there is a bit of
rubbing; that means, the fluid that has been
captured
there, experiences a shared traction, a share
between the layer that is sticking to the
surface of the fluid of the shroud or the
back plate and the other layer, which is being
intended or being carried or being pulled
by the rotating impeller.
So, this being captured on one side and being
pulled from the other side creates traction
in that fluid, which creates large amount
of rubbing losses. And then, of course you
have
a very large amount of turbine exit energy,
which always increases with the specific
speed or the speed. And, as a result of this
you can see towards the end, there is a large
amount of exit energy, which is not utilized
by the turbine.
So, if you take out all the actual losses
over the vanes, then your total-to-total efficiency
would have been something like this, and would
have continued to increase with the
specific speed.
So, total-to-total efficiency, which includes
the kinetic energy content of the outgoing
gas, actually increases with the specific
speed. On the other hand, the total-to-static
efficiency starts dropping after a certain
time and as a result of which, as you have
done
in the earlier lectures, in many turbine applications
the total-to-static efficiency becomes
an important consideration both for design
as well as for operation. And, as a result
of
this, one can see that one may need to peak
total-to-static efficiency as operating point,
which is not the peak total-to-total efficiency,
which is somewhere over here.
So, the differences in the two efficiencies,
actually are also figuring in the design
selection and in the design choices because
they have borne out of the losses and the
kinetic energy content of the outgoing gas.
Now, let us take a look at another radial
turbine characteristic, which is efficiency
verses
speed or specific speed. Now, the maximum
total-to-static efficiency as you have seen
starts falling. As we have seen in the last
diagram, it starts falling here and it peaks
somewhere over here. And, the maximum total-to-total
efficiency as we saw in the last
slide keeps going up like that. The stator
exit flow angle alpha 2, which as we all know
is
a very important parameter for turbine design
and also radial inflow turbine design,
actually it has a high impact on everything
that is happening. And, here that angle has
been factored in as one of the primary parameters
for design considerations.
So, it starts off with the higher angle of
83, 80 and then 74 and 68 and 62 and 56 and
52.
So, these are the angles. Quite often, the
choice is somewhere between 62 and 74. And
in
this particular case, for example, it shows
that somewhere around 74 degree is alpha 2
and somewhere over here you have the peak
of the maximum static total-to-static
efficiency, eta T S. And, that could be a
good design choice at which the dimensionless
specific speed is something like 0.58 little
less than 0.60 and that, and then becomes
your
design choice.
Now, at that design choice, the other thing
that needs to be looked into is the diameter
ratio; the hub to shroud diameter ratio at
the exit face of the impeller, which as we
have
just seen that at the exit phase over here,
this is D H and this is D shroud. This ratio
is an
important parameter. The other important parameter,
which we look at just now is, the
the diameter ratio between D shroud to D 2,
that is, the tip of the impeller. So, these
two
diameter ratio between this point and the
shroud of the exit phase, and the diameter
ratio
between shroud and hub at the exit phase itself,
actually are important design
considerations. And, alpha 2 as we just saw
is the important consideration because that
creates the jet and that jet goes into the
radial impeller because the relative velocity
there
has to be radial. So, the flow is going into
the radial impeller completely radially. So,
relative velocity has to be radial, but the
absolute velocity there is very high. It is
a jet
that is being created by the stator nozzle.
So, if we look at all these characteristics
put into this diagram, we can see that at
the
peak over here, which we have identified as
the probable design point, the ratio of D
2 to
D S, that is, the tip of the impeller to the
shroud is point… D hub to D 2 is 0.70. So,
this
is something which has been created by number
of design people, who have looked into
various aspects of the design and have inferred
that if you put together some of these
numbers in terms of diameter ratio, in terms
of alpha 2, then you can arrive at a peak
efficiency in terms of eta T S. And, the efficiency
of the total-to-total is still very good;
it
is not really that bad. So, it is somewhere
near the peak of total-to-total efficiency.
So,
you get a good efficient turbine design. So,
these parameters have been put together by
the designer over the years. And, this kind
of plot is a generalized plot. It is available
for
selection of your turbine fundamental parameters.
So, if we put together many of these things
that we have just shown, we can start our
discussion on the design of radial inflow
turbines. Now, design of a radial turbine
is
often an exercise in selection of the size
and shape of the vanes, both the stator nozzle
as
well as the complicated shape of the rotating
impeller. And, the shapes put together
should maximize the performance and minimize
the losses. So, we had a look at how the
losses vary with dimensionless speed and we
have to ensure that it produces the work.
The work that runs a compressor or any other
load that needs to be maximized. So, that
is the purpose of the turbine. And, for it
to be competitive in the market, for it to
compete
with the axial flow turbines, which of course
as we know are producing, very high work
these days due to the cooling technology.
And, we have seen that the radial inflow
turbine has to be competitive with those technologies
to hold its own. So, you have to
maximize the work done and somewhere along
the way, we have to ensure as we have
just seen that you are somewhere near the
peak of the efficiency.
If you remember the efficiency parameters
that we have done in case of actual flow
turbine, the efficiencies were those axial
flow turbines where actually higher. The
efficiencies of the radial flow turbines are
a few points less than that of axial flow
turbines. Now, this is in evitable because
we have a flow that is coming in radially
and
then going out axially. This, huge 90 degree
turn and over a larger surface of the rotor
or
impeller produces certain amount of inevitable
friction losses at high velocity jet;
because the flow is continuously accelerating.
And, as a result that kind of a loss through
the impeller vane as we have just seen in
the couple of slides back is inevitable.
So, the efficiency would always be few points
less in radial turbine than in case of axial
flow turbine. This is one of the reasons,
why the radial inflow turbine has not been
the
most popular choice of turbines even for small
gas turbines. People often choose axial
flow turbines simply because it is that 2
or 3 percentage more efficient in terms of
its
working capability. However, radial turbine
is a good machine. There is no question
about that. It is a robust machine. That is
also accepted. It normally does not have
cooling, but it produces reasonably good amount
of work with reasonably good
efficiencies and it has its uses. Towards
the end of today’s lecture, I will be able
to show
you a very special use of radial flow turbine
concept in very special applications.
So, the design of radial inflow turbine starts
with the selection of flow parameters. You
have to select the flow angle alpha 2, that
is, exit angle from the stator nozzle, which
produces jet at the velocity C 2. So, choice
of the angle alpha 2 we had seen in case of
axial flow turbines. Also, it is an important
design driver. So, here also alpha 2 is indeed
a strong design driver because it creates
a jet and then finally, ensures that the flow
going
into the turbine rotor is indeed radial. Then,
of course beta 3, which is made on the basis
of earlier design data bank; beta 3 is the
exit angle which goes out of the impeller.
And,
this angle is important because the absolute
velocity here going out should be axial.
So, the relative flow angle beta 2 has to
be of such an order that the absolute flow
angle
is 0. Now, this is again you need to ensure
by design. It is not going to happen by itself.
So, designer has to sit down and make sure
that under design conditions, these things
are
properly done. So, the flow in the relative
frame is going in radially; flow in the absolute
frame is going out at the exit phase in the
absolute frame actually. So, these are some
of
the issues that need to be looked into right
in the beginning of the design.
Then we will look at the geometrical parameters.
The geometrical parameters here are
the diameter ratio as we just saw, D 2 by
D 3 S, which is the shroud tip diameter, shroud
I tip diameter or the exit phase shroud diameter.
So, this ratio we just saw has a value
close to something like 0.70 or inverse of
that, and this about 1.3 or so. And, that
gives
rise to a selection criterion for the diameter
ratio. The other one is, of course as we saw
the exit hub tip to diameter ratio D 3 H to
D 3 shroud. And, these two need to be decided
because that fixes the size of the machine.
So, the size of the machine is fixed with
the
help of these two diameter ratios. Now, unless
you have some other restriction for
restricting the size of the impeller, these
two figures need to be chosen as early as
possible; even, if it other restrictions apply.
You have to choose them with reference to
those other restrictions where it is to be
applied.
Now, quite often radial turbines are indeed
used, where restrictions of size actually
been
applied. The utility of radial turbine is
that if you make a radial turbine that is
a restricted
size, let us say a very small one, it produces
still very high efficiency machine.
On the other hand, as we have discussed before
if you make the axial machines smaller
and smaller, the efficiency starts dropping.
So, axial compressor and axial turbine if
they
are very small, the three dimensional flow
inside those aerofoil shaped blades actually
bring down the efficiency of those things
and the aerofoil shape, which is a two
dimensional entity, fundamentally loses its
efficiency. And as a result, the efficiency
of
the entire machine in axial flow starts following
quite fast, when the size of the machine
starts becoming smaller and smaller.
So, when you have a small engine or a small
machine to be designed for a special
application, quite often people would go for
radial turbine or even centrifugal
compressor; because they are as I mentioned,
robust machines, they hold their efficiency
values even when they are very small in size.
One of the reasons of course, is that neither
of them deploys aerofoils in the rotating
vanes. So, rotating vanes are not made of
aerofoils, which as we have commented number
of times are aerodynamically fragile
shapes. So, the robust shapes are the non-aerofoil
shapes and the centrifugal machines,
the compressor and the turbine have that robustness,
which the axial flow machines
sometimes are lacking in, especially when
they are small in size. So, radial flow turbines
often, in a restricted space, again in space
craft applications or any other land based
applications or in special utility application,
even on board an aircraft, a radial flow
machines, often have very strong utility value
because they occupy less space and
produce a lot of work done per unit mass flow.
And then, of course the efficiency still
holds good. They do not drop so fast. So,
these are the reasons because of which the
centrifugal and the radial flow machines are
still preferred in many applications. In those
cases, these parameters need to be chosen
as early as possible.
The next parameter that we are looking at
is the flow coefficient. Now, flow coefficient
as defined here is axial flow at station three;
that is, at the exit to the U tip of the impeller
U 2. And, this is the flow coefficient, which
requires to be selected as early as possible
along with the work done or the pressure raise
or the pressure raise coefficient or as we
call the blade loading coefficient. So, those
things need to be chosen together. Now, flow
coefficient we have seen in case of earlier
machines, axial compressor, axial turbine,
centrifugal compressor is an important design
driver. So, flow coefficient again like
alpha 2 and the diameter ratios are a design
driver. Quite often, you choose your, many
of the design parameters in conjunction with
the flow coefficient. So, the flow coefficient
as defined here, as you can see it is slightly
different than in axial flow machine, but
that
is expected.
This flow coefficient is an important design
parameter. And then, of course putting all
of
them together you have a set of flow parameters,
you have a set of geometrical
parameters, which fixes the side size and
the shape of the machine. All of them together
constitute the design of your radial turbine.
.So, let us take a look at some of the issues
that are involved here. Now, in this figure
for
example, what has been captured is the tip
speed U 2 of the impeller, and then the inlet
temperature T 0 2 which is same as T 0 1,
coming into the radial turbine. And then,
of
course the various parameters; alpha 2 is
one parameter and then M 2 corresponding to
C
2, which could indeed go pretty close to sonic
mach number. And. So, at various mach
numbers of M 2 were, at various values of
alpha 2 specifically, this is been plotted
and as
you can see if the inlet temperature is going
up, one can go up to something like 1400 k,
the tip speed necessarily needs to be raised
to get the work actually to be done properly;
correspondingly, the values of alpha can be
selected from this particular graph.
Now, this graph is borne out of certain fundamental
theories. This is not an
experimentally obtained graph. So, it is borne
out of fundamental theories. So, this is a
kind of graph that allows you to make selection
of the design parameters. We have seen
you can select certain design parameters at
an efficiency of let us say point 87; that
gives
us a certain values of a diameter ratio that
we have seen before. And, this diameter ratio,
then leads us to value of U 2. T 0 1 or T
0 2 of course, is a design input from engine
thermodynamic cycle. Calculations and fixations
of the design point on that cycle, and
then together we can now, we should start
selecting what will be the value of alpha
2,
which is the exit from stator nozzle. So,
as we have seen, the alphas can be high of
the
order of 60 or 70. And, some of these are
50, 60, 70 when mach number is 1; 50, 60,
70
when Mach number is point 75 and 50, 60, 70,
alpha 2 when mach number is point 50.
These are the constant alpha lines. So, at
any constant alpha line, as temperature goes
up
your U 2 has to go up. As we can see finally,
with high Mach number flow, the value of
U 2 could be as high as 500 meters per second
tip speed. Now, this tells us, what the
design parameters are; in terms of the flow
speed, in terms of the rotational speed of
the
impeller. Because U 2 would immediately fix
the revolutions per minute, since we have
already tried to fix the diameters through
the diameter ratios.
So, now, we are going into fixing the rotational
speeds. So, this kind of selection process
and this as I mentioned is actually a theoretical
graph; not an empirically or
experimentally produced graph. So, this directly
allows you a design selection in terms
of the fundamental design drivers alpha 2,
T 0 2. So, you are now in in a position to
fix
the rotating speed of the impeller.
.The next thing that we can summarize is that
the exit flow at the rotor exit is axial.
Now,
as we have mentioned number of times, it is
an ideal design condition. So that, the flow
goes out actually, any world component there,
that means, a non-axial component of the
flow is going to be wastage of energy. And,
that energy will not be diffused through the
diffuser. The diffuser diffuses the actual
component. It will not diffuse the peripheral
or
old component or tangential component. And
as a result, the turbine performance would
suffer through wastage of energy in old component.
One simple design that one can
proceed with, as we have mentioned is that
from the earlier characteristics plots, the
diameter ratio D 3 h by D 3 shroud is normally
of the order of 0.40 near about or a little
higher than that. And, on the other hand,
D 3 shroud to D 2, that is, the tip diameter
of
the impeller is of the order of 0.70, the
inverse of which was around 1.3 or there about.
Now, these are numbers that people have been
using for a long time. And, have found
that you can get efficiency of the order of
87 percentages using some of these standard
design features. The other parameter that
one can look at is the blade tip speed to
spouting velocity ratio U 2 to C o. C o you
have done in the earlier lectures. And, the
flow coefficient at the rotor exit which is
C a 3 by U 2, which we introduced also in
the
last slide.
So, this tells us that you can have a selection
of these flow parameters. The earlier point
was about the geometrical parameters. Now,
we can select the flow parameters, using the
parameters that have been introduced before
including the spouting velocity.
And, we get a graph something like this. Now,
this allows us that U 2 by C o is plotted
over here, the flow coefficient is plotted
over here, and these are the efficiencies,
which
are the total-to-static efficiencies. So,
as you can see these are curvilinear elliptical
kinds
of plots. So, as you go inwards, the efficiencies
goes higher and higher. And, quite often
as we have seen a good 87 percentage efficiency
design can be achieved, if you choose
certain parameters as per some of the specifications
or prescriptions that we have been
talking about.
So, the prescriptions that we have been talking
about do produce reasonably efficient
machines. And from, which you can now choose
your U 2 by C o and C a 3 by U 2, so
very high flow coefficient for example, actually
produces low efficiency turbine.
Similarly, very low flow coefficient will
also produce low efficiency turbine; very
high
U 2 by C o will again produce low efficiency
turbine; and very low values of U2 by C o
will also produce low efficiency turbine.
So, one needs to have a good kind of a mean
optimized value of both these flow parameters,
to arrive at a good efficient turbine
design.
We can take a look at some of the issues related
to selection of the number of vanes in an
impeller. Finally, you have to do that. There
are two, three, correlation that people have
been using over the years. One is correlation;
in which you can see the number of vanes
keep going up with the increase of absolute
flow angle. So, when the flow angle goes
above 70, the number of vanes becomes very
high. Now, up to 20 also it is ok.
Absolute low angle of the order of 74, 75
is used indeed quite often, but after that,
as per
this correlation your number of vanes would
indeed go very high and that may not be a
good idea. On the other hand, the other correlation
which is available, keeps the number
of vanes not very high. So, towards the lower
values of alpha 2 below70, the number of
vanes is modest. And, you do not need a large
number of vanes. A correlation three
agrees with a correlation two over some of
the flow angles, but later on, it also prescribes
very high number of vanes. So, very high number
of vanes has a number of issues that
needs to be looked into.
So, what happens is if you have very high
number of vanes, you have very large surface
friction losses. Now, very large surface friction
losses are not a good idea because it is
going to give you low efficiency. On the other
hand, a certain number of vanes are
required to turn the flow from; you know whatever
angle is coming in beta 2 to beta 3.
And, this large flow turning is indeed required.
And, it is also required for good flow
guidance through the rotating vanes, before
it is exiting from the turbine. This guidance
is required for extraction of work or energy
for producing work. So, the numbers of
vanes needs to be optimized between large
surface friction loss and a good guidance
and
turning, that is required in the vanes. So,
the earlier parameter in earlier selection
criterion that we are looking at tells us
that correlation two is often a good prescription
because it gives a modest number of vanes,
even with raising absolute flow angle which
is a primary design driver. So, correlation
two is most used correlation for radial flow
turbine design; because it prescribes a reasonable
number of vanes, even with raising
flow exit flow angle from the stator nozzle.
The other parameter, which of course, is borne
out of the number of vanes, is of course,
the solidity which is given as, Z into L by
D 2 whereas; one is the curvilinear length
of
the rotor vane. Remember, the rotor vane has
a long curvilinear path. Now, this long
curvilinear path has to be decided how long
it should be? It depends on the… as we have
just seen; depends on the number of vanes
and it depends on the angle, through which
the flow would be turning. And, of course
the flow would be guided through those
passages. And, that passage if you remember,
this is a turbine. So, the passage is going
to
be a converging passage. So, it will be a
continuously converging passage, through
which the flow would be also turning in a
curvilinear path; so, it is a curvilinear
converging passage, through which the flow
will have to be accelerated in a guided
manner and if you can do that in a rotating
frame, you get work extraction.
So, solidity is a parameter that captures
all these geometrical features into one single
number. And, as we have seen in axial flow
machines, also solidity is an important
design parameter that needs to be decided.
Some are during the design. To ensure that,
you have sufficient number of vanes or blades
to do the work, but not too many to create
flow abstraction, flow blockage and high surface
friction.
.
.So, we will look at the selection of these
solidity parameters through another plot,
which
is again plotted with the help of various
theories and these tell us that, if you optimize
the
efficiency with the real efficiency, and then
you select the solidity parameter as one can
see here. The ratio of the radius of the impeller
r 2 to r 3 mean. Of course, it is the mean
radius at the exit of the rotor or impeller.
And, this radius ratio is similar to the diameter
ratio that we have done earlier; borne out
of that. It tells us that, you need to select
this in
conjunction with the solidity and then in
conjunction with the efficiency, which is
related
to the optimized efficiency.
So, this allows us to select the solidity.
So, you can see the radius ratio. If it is
somewhat
lower, your solidity parameter will have to
select to get a high efficiency to go for
a high
solidity to get a reasonable efficiency. On
the other hand, at high values of r 2 by r
3, if
though that is very high, then even with lower
solidity your efficiency starts coming
down. So, if with high or 2.0 or 3.0, the
general tendency is the efficiency is going
to
come out to be lower value. This is where,
you get high efficiencies. And, depending
on
what solidity you have, you get a reasonable
efficiency figure as a part of your design
exploration to begin with. Of course, you
have to find the efficiency later on through
CFD and through Rig testing. So, this plot
essentially gives you a good idea about what
you are. Solidity of the vane should be with
reference to selection of efficiency and the
radius ratio or the diameter ratio that we
have done before.
.Now, with the help of these geometrical and
other parameters, we can complete the go
towards completion of the design process of
radial in flow turbine. Now, you can use all
the graphs and plots, which if you have more
data bank available with you. You can get
a
good first cut design. You can improve your
design with the help of these graph,
immensely to get efficiencies easily of the
order of 84, 85 percentage. And then, if you
have to proceed towards higher values, you
can use CFD, which normally gives you fine
tuning of the efficiency and other geometrical
parameters, vane shapes. You can fine
tune them, but normally that is fine tuning.
If you want a lot of improvement that has
to
be done at the design stage itself through
the design procedure that we were talking
about. CFD gives fine improvement. It does
not give a very large improvement. And,
CFD of course, cannot be used for basic design.
CFD is, when you have a design and the
geometry is available and it lends itself
to CFD analysis.
The other parameter, the other point that
you need to keep in mind, is what is mentioned
here that radial turbines are normally not
cool turbines. The cooling technology has
not
been deployed in radial turbines. It is possible
that in future, we will have cooled radial
turbines. And as a result, the work capability
of the radial turbines will go up, but the
tip
of the radial turbine rotor, for example,
vane is rather thin and does not have any
provision for cooling. The stator nozzle of
course, can be thick and that can be cooled
and that cooling technology is now being explored.
And, if cooling can be deployed in
the stator nozzles vanes, then the radial
turbine working capability, its inlet temperature
can indeed be increased further, to get more
work done out of radial turbine.
So, cooling technology is something, which
is in the offing. And, if it is available,
radial
turbines would be more competitive, especially
in the small sized machines compared to
axial flow turbines.
Now, these are the basic design features of
radial inflow turbine. Let us, take a look
at a
very special case of radial inflow turbine
that has been used very successfully in creation
of micro gas turbines. In micro gas turbine,
the size of the gas turbine as you can see
here
is 21 millimeters. It is a very small machine.
It is 21 millimeters, that is, 2.1 centimeter
and it is only 3.7 millimeter thick. So, it
is like a button of your blazer or a coat
and it is
as small as a button. It is a button sized
gas turbine engine. What it is doing is the
flow is
coming in, here through this inlet system,
and then you have a compressor which is
typically a centrifugal compressor. We will
have a look at it right in a few minutes.
It is
basically a centrifugal compressor, but it
is very thin. As you can see, it is less than
1
millimeter thin and that drives a flow through
this blue line and it comes in.
In this zone, yellow zone, so the blue line
is of course, the flow coming in and it goes
into the combustion chamber. So, in the yellow
zone, the flow is indeed mixed with a
fuel and combusted, and then the combusted
fuel is then taken through the turbine. So,
this is the turbine and then this red is the
combusted flow that is, coming through the
turbine and finally, exhausted.
So, it comes from all sides. So, yellow zone
is shown in both sides. It is an annular
configuration; both the compressor as well
as the combustion chamber as well as the
turbine. So, compressor combustion chamber
and turbine are all housed within 3.7
millimeter thickness and 21 millimeter diameter
machine.
The compressor turbine as you can see is essentially,
back to back. So, turbine directly
runs the compressor because they are back
to back attached to each other. There was
a
little problem in the design, regarding the
turbine being hot and the compressor being
cold; however, little insulation here probably,
solved that problem.
So, this is a kind of a real micro machine
that people have already invented and has
been
found to be working with a reasonable working
capacity. This is a kind of replacement of
small energy producing or work producing machine.
Let us, take a look at a little more detail
of this machine. You have the compressor blades
over here. This is one half. So, this is 10.5
millimeter. So, you have one half of the
machine. So, it is just a little more than
1 centimeter, this whole thing. And, each
of them
is made of wafer. So, they are very thin.
So, you have the fuel injector here, you have
the
compressor blade and the air is coming in,
so the air fuel is mixed over here. And, this
air
fuel mixer goes in, it goes into the combustion
chamber, then it is delivered through the
stator nozzles into the turbine and finally,
it gets ejected. So, these are wafer thin.
So,
that is why, they are called wafer one, two,
three, four, five, six. Six Wafers are
essentially pasted on top of each other to
create a 3.7 or a 3.8 millimeter thick micro
gas
turbine. So, this is a kind of micro gas turbine
that has been created and is found to be
working.
This is the picture of the compressor and
the turbine. This is how the compressor works.
So, the compressor essentially is centrifugal
compressor. It rotates this way and throws
the flow out as you can pretty well see here.
The flow is diffusing through this and it
is a
rotational mode, the rotor is rotating. And
then, when it is rotating, it ejects a flow
out
and then this is a straighter way through
which the flow gets further diffused. That
diffused flow or compressed flow is delivered
into the combustion chamber and then it
comes to the turbine which, as we have seen
are back to back through the turbine. This
is
the stator nozzle through which the flow gets
hugely accelerated. So, this acceleration
occurs over here.
Clearly aerofoils have been deployed both
in compressor as well as in turbines. In
normal radial turbines and centrifugal compressors,
we have seen aerofoils are not
deployed. But, this is a very special machine
in which aerofoils have been deployed.
And, flow coming in, be the huge jet and then
that creates the motion of the turbine.
So, this rotation of the turbine rotor then
rotates the compressor itself. So, the rotor
spins
in anti-clockwise. This is rotating in this
direction and rotates a compressor along with
it.
So, typical aerofoil that we have seen in
case of axial flow turbines are actually deployed
over here in micro sizes. You can well imagine
how small these individual aerofoils are
because the whole thing is only about 2.1
centimeter are thereabout. So, they are
extremely small sized entities and these entities
are put together to what is called a micro
gas turbine. They are very small, but they
produce power to the tune of few watts, the
order of 10, 20 watts. That is good enough
to run a few appliance likes electronic
machines, communication systems, essentially
as a replacement of battery.
So, it is a very special application of radial
flow turbine. And, so radial flow turbine
has
lot of potential in terms of it; it is the
way its principles and the way it works and
is a
robust machine and creates good efficient
machines. So, we had a good look at the
various kinds of machines over the last thirty
five, thirty six lectures through axial
compressors, axial turbines, centrifugal compressor
and then finally, radial turbines.
And, we had a look at how some of these entities
could be designed. The first cut design
features have been discussed in our lecture
series and we are in a position now to create
these machines for usage.
In the next few lectures, we will be looking
at usage of CFD in fine tuning these designs.
How computational fluid dynamics is indeed
brought into the modern design, how the
design finally, becomes more efficient and
definitely more work producing power
producing machine. So, in the next few lectures,
we will be looking at CFD of
Turbomachinery that is, something we will
be doing over the next two or three lectures,
which are the final lectures in our lecture
series.
So, in the next lecture we are starting with
CFD of turbo machines.
