Download Lecture 21: Axial Flow Turbine - Degree of Reaction, Losses and Efficiency and more Slides Turbomachinery in PDF only on Docsity!

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In this lecture...

• Axial flow turbine
  • Degree of Reaction, Losses and

Efficiency

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Velocity triangles

U

C (^1)

V (^3)

V (^2)

C (^2)

Rotor

Stator/Nozzle

β 3 3

β 2

α 1

α 3

α 2

U

C (^3)

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Degree of reaction

Also, since h h U(C C )

h h (V V ) (V V )(V V )

of therotor, thisbecomes,

If the axialvelocity is the sameupstreamanddownstream

V V h h

apparent stagnationenthalpyis constant,

Since,in acoordinate system fixedto therotor, the

h h

h h

Stagnationenthalpy dropin the stage

Static enthalpy drop in therotor R

w w

2 w w w w w w

2

x

01 03 2 3

2 3 2 3 2

(^21) 2

2 2 3

1 3

2 2

2 3 3

01 03

2 3

2 2

− = −

− = − = − +

− = −

−

−

=

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Degree of reaction

is lower than that of a50% reaction stage.

higher and that is one of the reason why its efficiency

impulse turbine stage, all the flow velocities are

ratio than does the 50% reactionstage.In the

turbine stagerequires amuchhigher axial velocity

For agiven stator outlet angle, theimpulse

When, V V , R Impulse turbine

symmetrical triangles, , R..

It canbe seen that for aspecial caseof

w w X

2 X

3 2

α β 3

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Impulse turbine stage

U

V (^2)

V (^3)

V (^3)

C (^2)

Stator/Nozzle Rotor

β 3

α^ β^2 2

α 3

C (^3) C (^2)

α 2

V (^2)

β 2

U

β 3

C (^) a

C (^) w

C (^) w

V (^) w

V (^) w

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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.

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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.

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Efficiency

[ ] [ ]

γ γ γ γ

η

( )/ ( ) /

s

ts

T,ideal P s

(P /P )

(T /T )

T (P /P )

T T

T T

T T

The total- to- static efficiency is defined as

W c (T T )

Theideal turbine work withno exhaust KE wouldbe

1 3 01

03 01 1 01 3 01

01 03

01 3

01 03

01 3

− − −

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Efficiency

[ ] [ ]

γ γ γ γ

η

( )/ ( ) /

s

ts

T,ideal P s

(P /P )

(T /T )

T (P /P )

T T

T T

T T

The total- to- totalefficiency is defined as

W c (T T )

Theideal turbine work in suchcaseswouldbe

in suchmachines.

not consideredaloss as this is converted to thrust

Inmany applications(turbojets),the exhaust KEis

1 03 01

03 01 1 01 03 01

01 03

01 03

01 03

01 03

− − −

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Efficiency

Influence of loading on the total-to-static efficiency

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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.

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Losses in a turbine

Variation of profile loss with incidence

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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.