3. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Turbine Blade Profile
3
A typical turbine blade is an airfoil shaped
and are twisted from hub to tip with an
angle called stagger angle.
4. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Analysis of Work done
4
The Euler turbine equation relates the power added to or removed from the flow,
to characteristics of a rotating blade row. The equation is based on the concepts
of conservation of angular momentum and conservation of energy.
There is a change in angular momentum (as the
fluid passes through the impeller imparting torque to
it.
To derive the Euler Equation, let us consider a
control volume surrounding an impeller. The control
surface may be taken away from the rotor such that
the properties can be assumed uniform and
axisymmetric.
5. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Analysis of Work done
5
The flow enters the CV with tangential velocity and
leaves with tangential velocity . Let be the mass
flow rate and r1 and r2 be the radial distances at inlet
and outlet respectively.
AA’ is the axis of rotation.
• Moment of momentum exiting the CV is:
• Moment of momentum entering the CV is:
Thus, in a 1D steady flow, moment of momentum
flux out of the CV is:
6. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Analysis of Work done
6
For a pump or compressor rotor running at an
angular velocity , the rate at which the rotor does
work on the fluid is:
Where, U= r (blade speed)
Depending on the direction of U2 with reference to
U1, the sign will be +ve and –ve.
Hence, the work done on the fluid per unit mass or
specific work is:
This eqn is known as Euler Turbine Equation.
7. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Analysis of Work done
7
• If , then is +ve.
It is applicable to power absorbing turbo machine
like pump, fans, blower and compressor.
• If , then
• It is applicable to power generating turbo
machines or turbines.
• Thus, the work done per unit mass for
compressible flow is given by,
Turbine:
Compressor:
8. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Analysis of Work done
8
For incompressible flow, the work done per unit volume is given by,
Turbine:
Compressor:
The work done per unit weight:
Turbine:
Compressor:
9. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
9
• Steam turbines are usually impulse or a mixture of impulse and reaction
stages whereas gas turbines tend to be always of the reaction type.
• Pressure ratio of steam turbines can be of the order 1000:1, whereas it’s
within the order of 10:1 for gas turbines.
• To reduce the number of stages, pressure drop per stage should be
large, but in doing so blade losses and efficiency costs rise.
• Therefore, reaction stages are used where pressure drop per stage is
low and also where the overall pressure ratio of the turbine is relatively
low.
• Shape and size of the blades can vary with different types of stages.
10. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
10
• Turbine blades are of two basic types:
• A turbine composed of blades alternating with fixed nozzles is called an
impulse turbine, Curtis turbine, Rateau turbine.
• Nozzles appear similar to blades, but their profiles converge near the
exit. This results in a steam pressure drop and velocity increase as
steam moves through the nozzles.
• Nozzles move due to both the impact of steam on them and the reaction
due to the high-velocity steam at the exit.
• A turbine composed of moving nozzles alternating with fixed nozzles is
called a reaction turbine or Parsons turbine.
11. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
11
• Except for low-power applications,
turbine blades are arranged in
multiple stages in series, called
compounding which greatly
improves efficiency at low speeds.
• A reaction stage is a row of fixed
nozzles followed by a row of moving
nozzles.
• Schematic diagram outlining the
difference between an impulse and a
50 % reaction turbine.
12. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
12
• Multiple reaction stages divide the pressure drop between the steam inlet and
exhaust into numerous small drops, resulting in a pressure- compounded turbine.
• Impulse stages may be either pressure-compounded, velocity- compounded, or
pressure-velocity compounded.
• A pressure-compounded impulse stage is a row of fixed nozzles followed by a row
of moving blades, with multiple stages for compounding. This is also known as a
Rateau turbine, after its inventor.
• A velocity-compounded impulse stage (invented by Curtis and also called a "Curtis
wheel") is a row of fixed nozzles followed by two or more rows of moving blades
alternating with rows of fixed blades. This divides the velocity drop across the stage
into several smaller drops.
• A series of velocity-compounded impulse stages is called a pressure- velocity
compounded turbine.
13. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
13
Velocity Compounding
• There are number of moving blades
separated by rings of fixed blades on
a common shaft.
• When the steam passed through the
nozzles where it is expanded to
condenser pressure. It's Velocity
becomes very high.
• This high velocity steam then passes
through a series of moving and fixed
blades. When the steam passes
over the moving blades it's velocity
decreases where the work is done.
• The function of the fixed blades is to
re-direct the steam flow without
altering it's velocity
14. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
14
Pressure Compounding
• There are the rings of moving blades
which are keyed on a same shaft in
series, are separated by the rings of fixed
nozzles.
• The steam at boiler pressure enters the
first set of nozzles and expanded partially.
• The kinetic energy of the steam thus
obtained is absorbed by moving blades.
• The steam is then expanded partially in
second set of nozzles where it's pressure
again falls and the velocity increase the
kinetic energy so obtained is absorbed by
second ring of moving blades. This
process repeats again and again.
• During entire process, the pressure
decrease continuously but the velocity
fluctuate as shown in diagram.
15. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
15
Pressure Velocity Compounding
• This method of compounding is the
combination of two previously discussed
methods.
• The total drop in steam pressure is divided
into stages and the velocity obtained in
each stage is also compounded.
• The rings of nozzles are fixed at the
beginning of each stage and pressure
remains constant during each stage as
shown in figure.
• The turbine employing this method of
compounding may be said to combine
many of the advantages of both pressure
and velocity staging.
• By allowing a bigger pressure drop in each
stage, less number stages are necessary
and hence a shorter turbine will be
obtained for a given pressure drop.
16. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Blade Profile and staging of turbine
16
• Staging of axial-flow compressor-turbine assembly is done in combination
of rotor and stators.
• For centrifugal compressors, the staging are the same as spools, for e.g.
one compressor-turbine coupled stage is linked through a single ‘spool’
hence also called a ‘single spool compressor/turbine’.
• For axial compressors, the staging is defined in terms of rows of stator-rotor
assembly, with a single such assembly referred to as a compressor stage.
Each stage can have a compression ratio in the range of 1.05~2 with an
efficiency of around 0.94.
• Hence, for axial compressors a single spool can contain several stages.
And spools (up to three) in combination can provide compression in the
range of 5-40.
17. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Efficiency in Impulse Turbine
17
• By the law of moment of momentum, the torque on
the fluid is given by:
• For an impulse turbine: r2 = r1 = r
• Hence, the tangential force on the blades is:
• The work done per unit time or power developed is:
• Where, ω is the angular velocity of the turbine, then
the blade speed is U= ω.r
• The power developed is then:
18. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Efficiency in Impulse Turbine
18
Blade efficiency
• Blade efficiency can be defined as the ratio of the work done on the blades to
kinetic energy supplied to the fluid, and is given by:
Stage efficiency
• A stage of an impulse turbine consists of a nozzle set and a moving wheel. The
stage efficiency defines a relationship between enthalpy drop in the nozzle and
work done in the stage.
19. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Efficiency in Impulse Turbine
19
• Nozzle efficiency is given by:
• where the enthalpy (in J/Kg) of steam at the entrance of the nozzle is h1 and the
enthalpy of steam at the exit of the nozzle is h2.
• Hence
Condition for maximum efficiency,
• For a given steam velocity work done per kg of steam would be maximum when
• As increases, the work done on the blades reduces, but at the same time
surface area of the blade reduces, therefore there are less frictional losses.
21. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Velocity Vector Diagram in Reaction Turbine
21
• The axial turbine stage comprise a row of fixed
guide vanes or nozzles (often called a stator
row) and a row of moving blades or buckets (a
rotor row).
• Fluid enters the stator with absolute velocity C1
at angle α1.
• The rotor inlet relative velocity w2, at an angle
β2, is found by subtracting, vectorially, the
blade speed U from the absolute velocity C2.
• The relative flow within the rotor accelerates to
velocity w3 at an angle β3 at rotor outlet.
22. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Velocity Vector Diagram in Reaction Turbine
22
• Corresponding absolute flow parameters (C3, α3) is
obtained by adding, vectorially, the blade speed U to
the relative velocity w3 .
• Force on rotor
• Work done on blade
• Axial thrust on rotor
23. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
23
Degree of Reaction (R)
• The degree of reaction of a reaction turbine is
defined as the ratio of the enthalpy drop in moving
blades to the total enthalpy drop in the stage.
Where, h0 h1 h2 are Enthalpy of the steam at inlet of
fixed blades, at entry of moving blades, and at exit from
the moving blades respectively.
• The total enthalpy drop in a stage = Enthalpy drop in
fixed blades+ enthalpy drop in moving blades
24. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
24
Degree of Reaction (R)
• The total enthalpy drop for a stage is equal to work
done by the steam in the stage and it equals to,
• Pressure and enthalpy drop both in the fixed or
stator blade and moving blade:
25. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
25
Degree of Reaction (R)
• A very widely used design has half degree of reaction or 50% reaction and this is
known as Parson’s Turbine. This consists of symmetrical stator and rotor blades.
• The velocity triangle are symmetrical and we have:
27. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
27
Blade Efficiency
• Energy input to the blades in a stage,
28. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
28
Blade Efficiency
• From the inlet velocity triangle we have,
• Work done per unit mass flow,
• Hence, the blade efficiency
• For symmetrical triangles we
have:
29. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
29
Condition of maximum blade efficiency
For maximum efficiency,
From which finally yields
• Absolute velocity of the outlet at this stage is axial (see figure above). In this case
the energy transfer is
30. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Reaction Turbine
30
Condition of maximum blade efficiency
• can be found out by substituting the value of
in the expression for blade efficiency:
The blade efficiency for impulse turbine is:
• is greater in reaction turbine. Energy input per
stage is less. So there are more number of
stages in a reaction turbine.
31. Prepared By:
Asst. Prof Bibek
Dhungana
(Turbo Machine)
Comparison of efficiency in impulse and reaction turbine
31
• The variation of diagram efficiency with the blade speed ratio, U/V1 for the simple
impulse turbine and a reaction stage shown in figure.
• The efficiency curve for reaction turbine is flat for maximum value of the blade speed
ratio.
