Post on 05-Feb-2021
1
Lect- 21
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 2
Lect-21
In this lecture...
• Axial flow turbine• Degree of Reaction, Losses and
Efficiency
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 3
Lect-21
Degree of reaction
• Acceleration takes place in both rotor and the stator.
• Enthalpy drop in the rotor as well as the stator.
• Degree of reaction provides a measure of the extent to which the rotor contributes to the overall enthalpy drop in the stage.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 4
Lect-21
Velocity triangles
U
C1
V3
V2C2
Rotor
Stator/Nozzle
1
2
3β3
β2
α1
α3
α2
U
C3
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 5
Lect-21
Degree of reaction
)CC(Uhhcesin,Also
)VV)(VV()VV(hhbecomes, this rotor, the of
downstream and upstream same the is velocity axial the If
VVhh
constant, is enthalpy stagnation apparent the rotor, the to fixed system coordinate a in Since,
hhhh
stage the in drop enthalpy Stagnationrotor the in drop enthalpy StaticR
ww
wwwwww2
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3
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32
22
−=−
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−=−
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=
=
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 6
Lect-21
Degree of reaction
+−=
−=
=
+−=
−=−
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=
)tan(tanUCRthatso
UtanCVandtanCV,thatknowWe
U)VV(R,Therefore
)CC()VV(,Since)CC(U
)VV)(VV(R
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aw
aw
wwX
wwww
ww
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3221
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23
2323
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2
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βα
αβ
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 7
Lect-21
Degree of reaction
stage. reaction 50% a of that thanlower is efficiency its why reason the of one is that andhigher
are velocities flow the all stage, turbine impulse the In stage. reaction 50% the does than ratio
velocity axialhigher much a requires stage turbine impulse the angle, outletstator given aFor
turbinepulseImR,VV,When..R, triangles, lsymmetrica
of case special afor that seen be can It
Xww
X2
→=−=
=−=
050
23
3βα
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 8
Lect-21
Impulse turbine stage
U
V2
V3
V3
C2
RotorStator/Nozzle
1 2 3
β3
β2α2
α3
C3 C2
α2
V2
β2
U
β3
Ca
Cw2
Cw3
Vw3
Vw2
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 9
Lect-21
50% Reaction turbine stage
RotorStator/Nozzle
1 2 3
U
V2
V3
V3
C2
β3
C3 C2
α2
V2
β2U
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 10
Lect-21
Efficiency• We noted that the aerodynamic losses in
the turbine differ with the stage configuration, or the degree of reaction.
• Improved efficiency is associated with higher reaction, which implies less work per stage and therefore a higher number of stages for a given overall pressure ratio.
• The understanding of losses is important to design, not only in the choice of the configuration, but also on methods to control these losses.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 11
Lect-21
Efficiency• There are two commonly used turbine
efficiency definitions.• Total-to-static efficiency• Total-to-total efficiency
• The usage of the efficiency definition depends upon the application.
• In land-based power plants, the useful turbine output is in the form of shaft power and exhaust KE is a loss.
• In this case the ideal turbine process would be isentropic such that there is no exhaust KE.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 12
Lect-21
Efficiency
s
T01
1
203
2s
3s
303s
P01P1
P2
P03P3
pcC2
23
Expansion process in a turbine stage
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 13
Lect-21
Efficiency
[ ] [ ]γγγγ
η
/)(/)(
sts
sPideal T,
)P/P()T/T(
)P/P(TTT
TTTT
as defined is efficiency static-to-total The)TT(cW
be would KE exhaust no withwork turbine ideal The
1013
01031
01301
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301
0301
301
11
1 −− −−
=−
−=
−−
=
−=
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 14
Lect-21
Efficiency
[ ] [ ]γγγγ
η
/)(/)(
sts
sPideal T,
)P/P()T/T(
)P/P(TTT
TTTT
as defined is efficiency total-to-total The)TT(cW
be would cases such inwork turbine ideal The machines. such in
thrust to converted is this as loss a considered notis KE exhaust the ),(turbojets nsapplicatio many In
10103
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 15
Lect-21
Efficiency
[ ]
−=
−=
>
−−=
=−≅−
−− γγγγ
ηη
ηη
ηη
/)(
01ptst
/)(
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:wayfollowingtheindoneworkspecificthetorelatedbealsocansdefinitionefficiencyThe
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 16
Lect-21
Efficiency
Influence of loading on the total-to-static efficiency
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 17
Lect-21
Losses in a turbine• Nature of losses in an axial turbine
– Viscous losses – 3-D effects like tip leakage flows, secondary
flows etc.– Shock losses– Mixing losses
• Estimating the losses crucial designing loss control mechanisms.
• However isolating these losses not easy and often done through empirical correlations.
• Total losses in a turbine is the sum of the above losses.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 18
Lect-21
Losses in a turbine• Viscous losses
– Profile losses: on account of the profile or nature of the airfoil cross-sections
– Annulus losses: growth of boundary layer along the axis
– Endwall losses: boundary layer effects in the corner (junction between the blade surface and the casing/hub)
• 3-D effects:– Secondary flows: flow through curved blade passages– Tip leakage flows: flow from pressure surface to
suction surface at the blade tip– 3-D effects are likely to be stronger in a turbine blade
as compared to compressor blade due to high camber and flow turning
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 19
Lect-21
Losses in a turbine
Variation of profile loss with incidence
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 20
Lect-21
2-D Losses in a turbine• 2-D losses are relevant only to axial flow
turbomachines.• These are mainly associated with blade
boundary layers, shock-boundary layer interactions, separated flows and wakes.
• The mixing of the wake downstream produces additional losses called mixing losses.
• The maximum losses occur near the blade surface and minimum loss occurs near the edge of the boundary layer.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 21
Lect-21
2-D Losses in a turbine
• 2-D losses can be classified as:• Profile loss due to boundary layer, including
laminar and/or turbulent separation.• Wake mixing losses• Shock losses• Trailing edge loss due to the blade.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 22
Lect-21
Total losses in a turbine• The overall losses in a turbine can be summarised
as:
losses Endwall:loss leakage tip :
loss flow secondary:lossesshock :
losses profile :Where,
E
L
s
sh
P
ELsshP
ωωωωω
ωωωωωω ++++=
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 23
Lect-21
Deviation• Flow at the exit of the rotor does not leave
at exactly the blade exit angle.• It has been found from experience that the
actual exit angle at the design pressure ratio is well approximated by
• This is true as long as the nozzle is not choked.
• Under choked condition, a supersonic expansion may alter the flow direction at the exit.
)s/d(cos 12−=α
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 24
Lect-21
d
sα2
Flow at the nozzle exit
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 25
Lect-21
Flow at the nozzle exit in the presence of shocks
Trailing edge shock
Reattachment shock
Flowα2
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 26
Lect-21
In this lecture...
• Axial flow turbine• Degree of Reaction, Losses and
Efficiency
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 27
Lect-21
In the next lecture...
• Axial flow turbine• Performance characteristics• Exit flow matching with nozzle
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