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

Some concept of Turbomachinery Aerodynamics are Axial Flow Compressors, Axial Turbine Design Considerations, Blade Performance, Engine Performance Significantly, Flows Through Axial Compresso. Main points of this lecture are: Reaction Turbine Stages, Impulse, Reaction Turbine, Turbine Stages, Stage Dynamics, Blade Cascade, Turbine Blade, Axial Compressors, Nozzle/Stator, Fluid Imparts

Typology: Slides

2012/2013

Uploaded on 04/27/2013

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Download Reaction Turbine Stages - Turbomachinery Aerodynamics - Lecture Slides and more Slides Turbomachinery in PDF only on Docsity!

1

2

In this lecture...

• Axial flow turbine

• Impulse and reaction turbine stages

• Work and stage dynamics

• Turbine blade cascade

4

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

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.

7

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.

8

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)

10

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

11

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:

13

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

14

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

16

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.

17

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.

19

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.

20

Turbine Cascade

Inviscid flow through a turbine cascade