Axial flow turbine

Full lecture

1. 1
Lect-20

2. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-20
In this lecture...
•Axial flow turbine
•Impulse and reaction turbine stages
•Work and stage dynamics
•Turbine blade cascade

3. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
3
Lect-20
Axial flow turbines
•Axial turbines like axial compressors
usually consists of one or more stages.
•The flow is accelerated in a nozzle/stator
and then passes through a rotor.
•In the rotor, the working fluid imparts its
momentum on to the rotor, that converts
the kinetic energy to power output.
•Depending upon the power requirement,
this process is repeated in multiple stages.

4. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
4
Lect-20
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.

5. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
5
Lect-20
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.

6. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
6
Lect-20
Axial flow turbines
123
Hot gas Exhaust
Nozzle/stator
Rotor
Disc
An axial turbine stage

7. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
7
Lect-20
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, Cand 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
wor V
w)
•αdenotes the angle between the absolute velocity
with the axial direction and βthe corresponding
angle for the relative velocity.

8. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
8
Lect-20
Velocity triangles
U
C
1
V
3
V
2
C
2
Rotor
Stator/Nozzle
1
2
3β
3
β
2
α
1
α
3
α
2
U
C
3

9. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
9
Lect-20
Typesof axial turbines
•There are two types of axial turbine
configurations: Impulse and reaction
•Impulse turbine
•Entire pressure drop takes place in the
nozzle.
•Rotor blades simply deflect the flow and
hence have symmetrical shape.
•Reaction turbine
•Pressure drop shared by the rotor and the
stator
•The amount of pressure drop shared is given
by the degree of reaction.

10. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
10
Lect-20
Work and stage dynamics
01
32
01
0
030203010
030132
332
Tc
)CC(U
T
T
,isratioworkstageThe
TTTTTLet
)TT(cwor)CC(Uw
is mass unitper work the Therefore,
.UUU turbine, axial an In
)CUC(UmP
equation, momentumangular the Applying
p
ww
ptwwt
32
ww2
−
=
−=−=
−=−=
=≈
−=
Δ
Δ


11. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
11
Lect-20
Work and stage dynamics
U
CC
U
h
U
w
ww
22
t 320
−
==
Δ
•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:

12. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
12
Lect-20
Impulse turbine stage
U
V
2
V
3
V
3
C
2
RotorStator/Nozzle
1
2
3
β
3
β
2α
2
α
3
C
3
C
2
α
2
V
2
β
2
U
β
3
C
a
C
w2
C
w3
V
w3
V
w2

13. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
13
Lect-20
Impulse turbine stage






−=






−=
−==−
−=⇒−=
12
12
22
2
2232
2323
α
Δ
α
ββ
tan
U
C
U
U
h
is ratiowork turbine the ,Or
tan
U
C
U
)UC(VCCand
VV
, Thereforeflow. the
deflects simplyrotor the turbine, impulse an In
a
2
0
a
wwww
ww

14. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
14
Lect-20
50%Reaction turbine stage
RotorStator/Nozzle
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

15. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
15
Lect-20
Impulse turbine stage






−=
−−=
12
2
23α
Δ
α
tan
U
C
U
h
becomes ratiowork turbine the And
)UtanC(C
velocity, axial constantfor , Thereforel.symmetrica
are triangles velocity the turbine, reaction 50% a In
a
2
0
aw

16. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
16
Lect-20
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 bladinggeometry and measure
losses in the stagnation pressure.

17. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
17
Lect-20
Turbine Cascade
•Turbinecascades 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.
•Turbineblades 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.

18. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
18
Lect-20
Turbine Cascade

19. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
19
Lect-20
Turbine Cascade
•Fromelementary analysis of the flow through
a cascade, we can determine the lift and drag
forces acting on the blades.
•Thisanalysis could be done using inviscidor
potential flow assumption or considering
viscous effects (in a simple manner).
•Let us consider V
mas the mean velocity that
makes and angle
α
mwith the axial direction.
•We shall determinethe circulation developed
on the blade and subsequently the lift force.
•Inthe inviscidanalysis, lift is the only force.

20. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
20
Lect-20
Turbine Cascade
Inviscidflow through a turbine cascade

21. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
21
Lect-20
Turbine Cascade
m
m
wwm
m
L
wwmm
ww
cos)tan(tan
C
S
CV
)VV(SV
CV
L
C t,coefficien Lift
form, ldimensiona-non a in lift Expressing
)VV(SVVL,liftand
)VV(S,nCirculatio
ααα
ρ
ρ
ρ
ρΓρ
Γ
12
2
2
1
12
2
2
1
12
12
2 −=
−
==
−==
−=

22. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
22
Lect-20
Turbine Cascade
•Viscous effects manifest themselves in the
form to total pressure losses.
•Wakes from the blade trailing edge lead to
non-uniform velocity leaving the blades.
•Inaddition to lift, drag is another force that
will be considered in the analysis.
•Thecomponent of drag actually contributes to
the effective lift.
•We definetotal pressure loss coefficient as:
2
22
1
0201
V
PP
ρ
ω
−
=

23. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
23
Lect-20
Turbine Cascade
Viscous flow through a turbine cascade

24. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
24
Lect-20
Turbine Cascade
mDmL
mmm
mtanCcos)tan(tan
C
S
C
,tcoefficienliftthe,Therefore
cosSVcosSL
lifteffectiveThe
cosSD,bygivenisDrag
αααα
αωΓραω
αω
+−=
+=+
=
122

25. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
25
Lect-20
Turbine Cascade
•Based on the calculation of the lift and drag
coefficients, it is possible to determine the
blade efficiency.
•Bladeefficiency is defined as the ratio of ideal
static pressure drop to obtain a certain change in KE to the actual static pressure drop to
produce the same change in KE.
mL
D
b
D
mC
C
mC
C
bsinC
C
,definitionlifttheintermC the neglect we If
cot
tan
L
D
L
D
α
η
α
α
η
2
2
1
1
1
1
+
=
+
−
=

26. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
26
Lect-20
In this lecture...
•Axial flow turbine
•Impulse and reaction turbine stages
•Work and stage dynamics
•Turbine blade cascade

27. Prof. BhaskarRoy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
27
Lect-20
In the next lecture...
•Axial flow turbine
•Degree of Reaction, Losses and
Efficiency