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In this lecture...
• Axial flow turbine
• Impulse and reaction turbine stages
• Work and stage dynamics
• Turbine blade cascade
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Axial flow turbines
- Due to motion of the rotor blades two
distinct velocity components: absolute and
relative velocities in the rotor.
- This is very much the case in axial
compressors that was discussed earlier.
- Since turbines operate with a favourable
pressure gradient, it is possible to have
much higher pressure drop per stage as
compared with compressors.
- Therefore, a single turbine stage can drive
several stages of an axial compressor.
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Axial flow turbines
- Turbines can be either axial, radial or mixed.
- Axial turbines can handle large mass flow
rates and are more efficient.
- Axial turbine have same frontal area as that
of the compressor.
- They can also be used with a centrifugal
compressor.
- Efficiency of turbines higher than that of
compressors.
- Turbines are in general aerodynamically
“easier” to design.
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Velocity triangles
- Elementary analysis of axial turbines too begins
with velocity triangles.
- The analysis will be carried out at the mean height
of the blade, where the peripheral velocity or the
blade speed is, U.
- The absolute component of velocity will be
denoted by, C and the relative component by, V.
- The axial velocity (absolute) will be denoted by C (^) a
and the tangential components will be denoted by
subscript w (for eg, C (^) w or Vw )
• α denotes the angle between the absolute velocity
with the axial direction and β the corresponding
angle for the relative velocity.
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Velocity triangles
U
C (^1)
V (^3)
V (^2)
C (^2)
Rotor
Stator/Nozzle
1
2
β 3 3
β 2
α 1
α 3
α 2
U
C (^3)
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Work and stage dynamics
01
2 3
01
0
0 01 03 02 03
2 3 01 03
2 3 3
c T
U(C C )
T
T
The stage work ratio is,
Let T T T T T
w U(C C ) or w c (T T )
Therefore, the work per unit massis
Inanaxial turbine,U U U.
P m(U C U C )
Applying the angular momentum equation,
p
w w
t w w t p
2 3
2 w w
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Work and stage dynamics
U
C C
U
h
U
w w w
2 2
t 0 2 − 3
• Turbine work per stage is limited by
- Available pressure ratio
- Allowable blade stresses and turning
• Unlike compressors, boundary layers are
generally well behaved, except for local
pockets of separation
• The turbine work ratio is also often defined
in the following way:
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Impulse turbine stage
2
2 3 2 2
3 2 3 2
α
α
β β
tan U
C
U
U
h
Or, the turbine work ratio is
tan U
C
U
and C C V (C U)
V V
the flow. Therefore,
Inanimpulse turbine, the rotor simply deflects
a 2
0
a
w w w w
w w
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50% Reaction turbine stage
Stator/Nozzle^ Rotor
1 2 3
U
V (^2)
V (^3)
V (^3)
C (^2)
β 3
C (^3) C (^2)
α 2
V (^2)
β 2
U
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Turbine Cascade
- A cascade is a stationary array of blades.
- Cascade is constructed for measurement of
performance similar to that used in axial
turbines.
- Cascade usually has porous end-walls to
remove boundary layer for a two-dimensional
flow.
- Radial variations in the velocity field can
therefore be excluded.
- Cascade analysis relates the fluid turning
angles to blading geometry and measure
losses in the stagnation pressure.
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Turbine Cascade
- Turbine cascades are tested in wind tunnels
similar to what was discussed for compressors.
- However, turbines operate in an accelerating
flow and therefore, the wind tunnel flow driver
needs to develop sufficient pressure to cause
this acceleration.
- Turbine blades have much higher camber and
are set at a negative stagger unlike
compressor blades.
- Cascade analysis provides the blade loading
from the surface static pressure distribution
and the total pressure loss across the cascade.
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Turbine Cascade
- From elementary analysis of the flow through
a cascade, we can determine the lift and drag
forces acting on the blades.
- This analysis could be done using inviscid or
potential flow assumption or considering
viscous effects (in a simple manner).
- Let us consider V (^) m as the mean velocity that
makes and angle αm with the axial direction.
- We shall determine the circulation developed
on the blade and subsequently the lift force.
- In the inviscid analysis, lift is the only force.
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Turbine Cascade
Inviscid flow through a turbine cascade