Reaction Turbine Stages - Turbomachinery Aerodynamics - Lecture Slides, Slides of Turbomachinery

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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