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In this lecture...

• Design parameters
• Two dimensional analysis: Cascade

aerodynamics

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Degree of reaction

• Diffusion takes place in both rotor and the

stator.

• Static pressure rises 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 pressure rise in the stage.

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Degree of reaction

02 01

2 1

02 01

2 1

03 01 03 01

2 1 2 1

02 01

2 1

03 01

2 1

1

1

P P

P P

h h

h h R

and for the stage,h h P P

h h P P for therotor

For anearly incompressible flow,

h h

h h

h h

h h

Stagnation enthalpy risein the stage

Static enthalpy rise in the rotor R

x

x

−

− ≅ −

− ∴ =

− ≅ −

− ≅ −

−

− ≈ −

−

=

ρ

ρ

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Degree of reaction

• Special cases of Rx
  • R (^) x =0, , There is no pressure rise in the

rotor, the entire pressure rise is due to the

stator, the rotor merely deflects the incoming

flow: impulse blading

• R (^) x =0.5, gives , the velocity

triangles are symmetric, equal pressure rise in

the rotor and the stator

• R (^) x =1.0, , entire pressure rise takes

place in the rotor while the stator has no

contribution.

α 1 = β 2 and α 2 = β 1

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Degree of reaction

 - C U - C - V - V - β - β 

• α - α - C U - C - V - V - β - β - α - α - C U - C - V - V - β - β - α - α
  • β 2 = − β 1 α 1 = β 2 and α 2 = β - α 2 = − α
    • Rx =0.0 Rx =0.5 Rx =1.

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Diffusion factor

0 50 100

V (^2)

V (^1)

V (^) max

Suction

surface

Pressure

surface

Velocity

Percent chord

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Diffusion factor

• Lieblein (1953) proposed an empirical

parameter for diffusion factor.

• It is expressed entirely in terms of known or

measured quantities.

• It depends strongly upon solidity (C/s).
• It has been proven to be a dependable indicator of

approach to separation for a variety of blade

shapes.

• D *^ is usually kept around 0.5.

betweenthe blades.

Where,Cisthe chordof thebladeandsis thespacing

V

V

V

s

C

V

V

V D

w w

1

1 2

1

2

2

1

 

  



−

∗

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Cascade aerodynamicsCascade aerodynamics

• The cascade is mounted on a turntable so

that its angular direction relative to the

inlet can be set at different incidence

angles.

• Measurement usually consist of pressures,

velocities and flow angles downstream of

the cascade.

• Probe traverse at the trailing edge of the

blades for measurement.

• Blade surface static pressure using static

pressure taps: c p distribution.

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Cascade wind tunnel

Linear open circuit cascade wind tunnel

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Cascade nomenclature

χ

C

C

deflection angle

i incidenceangle

stagger

camber

t thickness

s spacing/pitch

C Chord

=

=

=

=

=

=

=

δ

χ

θ

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Cascade aerodynamics

• The cascade is mounted on a turntable so

that its angular direction relative to the

inlet can be set at different incidence

angles.

• Measurement usually consist of pressures,

velocities and flow angles downstream of

the cascade.

• Special nulling type probes (cylindrical,

claw or cobra type) are used in the

measurements.

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Performance parameters

• Blade performance/loading can be

assessed using static pressure coefficient:

• The C (^) P distribution (usually plotted as C (^) P

vs. x/C ) gives an idea about the

chordwise load distribution.

at the cascade inlet)

P is thereference staticpressure(usually measured

Where,P is the blade surface staticpressure and

V

P P C

ref

local

local ref P (^2) 2 1

1 ρ

−

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Performance parameters

Deflection, degrees

Total pressure loss coefficient

Position along cascade

Location of the blade trailing edge