1

Lect- 3

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 2

Lect-3

In this lecture...

• Design parameters• Two dimensional analysis: Cascade

aerodynamics

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 3

Lect-3

Design parameters

• The following design parameters are often used in the parametric study of axial compressors:– Flow coefficient,

– Stage loading,

– Degree of reaction, Rx

– Diffusion factor, D*

UCa /=φ

UCUh w // 20 ∆=∆=ψ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 4

Lect-3

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.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 5

Lect-3

Degree of reaction

( )

( )

0102

12

0102

12

01030103

1212

0102

12

0103

12

1

1

PPPP

hhhhR

PPhh stage, thefor and

rotor thefor PPhh

flow, ibleincompress nearly aFor hhhh

hhhh

stage the in rise enthalpy Stagnationrotor the in rise enthalpy StaticR

x

x

−−

≅−−

=∴

−≅−

−≅−

−−

≈−−

=

=

ρ

ρ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 6

Lect-3

Degree of reaction

)tan(tanU

CR or,

)tan(tanU

CR tion,simplifica On

CCVV And,VVVV velocity, axial constantFor

)CC(UVV

hhhhR

VhVh

equation, energy flow steady the From

ax

ax

wwww

ww

wwx

21

21

2121

22

21

22

21

12

22

21

0103

12

22

2

21

1

2

221

2

22

ββ

βα

+=

−−=

−=−

−=−

−−

=−−

=∴

+=+

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 7

Lect-3

Degree of reaction

• Special cases of Rx– Rx=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

– Rx=0.5, gives , the velocity triangles are symmetric, equal pressure rise in the rotor and the stator

– Rx=1.0, , entire pressure rise takes place in the rotor while the stator has no contribution.

1221 and βαβα ==

12 ββ −=

12 αα −=

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 8

Lect-3

Degree of reaction

U

C1

C2

V1

V2

β1

β2α2

α1

U

C1

C2

V1

V2

β1

β2α2

α1

U

C1

C2V1

V2

β1

β2α2

α1

1221 and βαβα ==12 ββ −=

12 αα −=

Rx=0.0 Rx=0.5 Rx=1.0

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 9

Lect-3

Diffusion factor• Fluid deflection (β2-β1)is an important

parameter that affects the stage pressure rise.• Excessive deflection, which means high rate of

diffusion, will lead to blade stall.• Diffusion factor is a parameter that associates

blade stall with deceleration on the suction surface of the airfoil section.

• Diffusion factor, D*, is defined as

edge. leading the at velocity the is V and edge trailing the at velocity ideal the is V and point pressure minimum the

at velocity surface ideal the is VWhere, V

VVD maxmax

1

2

1

2−=∗

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 10

Lect-3

Diffusion factor

0 50 100

V2

V1

Vmax

Suction surface

Pressure surface

Velo

city

Percent chord

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 11

Lect-3

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.

blades. the betweenspacing the is s and blade the of chord the is C Where,

VsC

VVVVD ww

1

21

1

2

21

−

+−=∗

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 12

Lect-3

Cascade aerodynamics• A cascade is a stationary array of blades.• Cascade is constructed for measurement of

performance similar to that used in axial compressors.

• 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.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 13

Lect-3

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: cp distribution.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 14

Lect-3

Cascade wind tunnel

Linear open circuit cascade wind tunnel

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 15

Lect-3

Cascade wind tunnel

Linear open circuit cascade wind tunnel

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 16

Lect-3

Cascade nomenclature

χ

C

C

angledeflectionangleincidencei

staggercamberthicknesst

pitch/spacingsChordC

=======

δ

χθ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 17

Lect-3

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.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 18

Lect-3

Performance parameters• Measurements from cascade: velocities,

pressures, flow angles ...• Loss in total pressure expressed as total

pressure loss coefficient

• Total pressure loss is very sensitive to changes in the incidence angle.

• At very high incidences, flow is likely to separate from the blade surfaces, eventually leading to stalling of the blade.

212

10201

VPPWPLC ρ

−=

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 19

Lect-3

Performance parameters• Blade performance/loading can be

assessed using static pressure coefficient:

• The CP distribution (usually plotted as CPvs. x/C) gives an idea about the chordwise load distribution.

inlet) cascade the at measured (usually pressure static reference the isP

and pressure static surface blade the is P Where,V

PPC

ref

local

reflocalP 2

121 ρ−

=

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 20

Lect-3

Performance parameters

Def

lect

ion,

deg

rees

Tota

l pre

ssur

e lo

ss c

oeffi

cien

t

Position along cascade

Location of the blade trailing edge

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 21

Lect-3

Performance parameters

β1

β2 β2

β1

C1

C2C2

C1 Stalled or separated flow

(a) Normal operation (b) Stalled operation

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 22

Lect-3

Performance parameters

Incidence angle, degrees

Tota

l pre

ssur

e lo

ss c

oeffi

cien

t

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 23

Lect-3

In this lecture...

• Design parameters• Two dimensional analysis: Cascade

aerodynamics

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 24

Lect-3

In the next lecture...

• 2-D losses in axial compressor stage –primary losses