Lect- 21 · 2017. 8. 4. · 22. Lect-21. Total losses in a turbine • The overall losses in a turbine can be summarised as::Endwall . losses: tip leakage loss:secondary flow loss:

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


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.


Lect-21

Velocity triangles

U

C1

V3

V2C2

Rotor

Stator/Nozzle

1

2

3β3

β2

α1

α3

α2

U

C3


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

2

x

320301

2323212

22

321

3

22

23

3

0301

32

22

−=−

+−=−=−

−=−

−−

=

=


Lect-21

Degree of reaction

+−=

−=

=

+−=

−=−

−+−

=

)tan(tanUCRthatso

UtanCVandtanCV,thatknowWe

U)VV(R,Therefore

)CC()VV(,Since)CC(U

)VV)(VV(R

aX

aw

aw

wwX

wwww

ww

wwwwX

3221

22

33

23

2323

32

2323

1

2

2

βα

αβ


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


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


Lect-21

50% Reaction turbine stage

RotorStator/Nozzle

1 2 3

U

V2

V3

V3

C2

β3

C3 C2

α2

V2

β2U


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.


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.


Lect-21

Efficiency

s

T01

1

203

2s

3s

303s

P01P1

P2

P03P3

pcC2

23

Expansion process in a turbine stage


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

0301

301

0301

301

11

1 −− −−

=−

−=

−−

=

−=


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

01031

010301

0301

0301

0301

0301

11

1 −− −−

=−

−=

−−

=

−=


Lect-21

Efficiency

[ ]

−=

−=

>

−−=

=−≅−

−− γγγγ

ηη

ηη

ηη

/)(

01ptst

/)(

01pttt

tstt

sp

tstt

p03ss03s

PPTcwand

PPTcw

:wayfollowingtheindoneworkspecificthetorelatedbealsocansdefinitionefficiencyThe

,thatseecanWe)TT(cC

,Therefore

c/CTTTT:ionapproximat an

making by efficiency of sdefinition two the compare can We

1

01

3

1

01

03

30123

2333

11

21

2


Lect-21

Efficiency

Influence of loading on the total-to-static efficiency


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.


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


Lect-21

Losses in a turbine

Variation of profile loss with incidence


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.


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.


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 ++++=


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


Lect-21

d

sα2

Flow at the nozzle exit


Lect-21

Flow at the nozzle exit in the presence of shocks

Trailing edge shock

Reattachment shock

Flowα2


Lect-21

In this lecture...

• Axial flow turbine• Degree of Reaction, Losses and

Efficiency


Lect-21

In the next lecture...

• Axial flow turbine• Performance characteristics• Exit flow matching with nozzle

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Lect- 21 · 2017. 8. 4. · 22. Lect-21. Total losses in a turbine • The overall losses in a turbine can be summarised as::Endwall . losses: tip leakage loss:secondary flow loss: