lect-14 · basic operation of axial compressors • turbines on the other hand operate under...

1

Lect-14

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay2

Lect-14

In this lecture...

• Axial flow compressors– Basic operation of axial compressors– Velocity triangles– Work and compression– Design parameters

• Flow coefficient• Loading coefficient• Degree of reaction• Diffusion factor


Lect-14

Basic operation of axial compressors• Axial flow compressors usually consists of a

series of stages.• Each stage comprises of a row of rotor

blades followed by a row of stator blades.• The working fluid is initially accelerated by

the rotor blades and then decelerated in the stator passages.

• In the stator, the kinetic energy transferred in the rotor is converted to static pressure.

• This process is repeated in several stages to yield the necessary overall pressure ratio.


Lect-14

Basic operation of axial compressors• The compression process consists of a series of

diffusions.• This occurs both in the rotor as well as the

stator. • Due to motion of the rotor blades two distinct

velocity components: absolute and relative velocities in the rotor.

• The absolute velocity of the fluid is increased in the rotor, whereas the relative velocity is decreased, leading to diffusion.

• Per stage pressure ratio is limited because a compressor operates in an adverse pressure gradient environment.


Lect-14

Basic operation of axial compressors

• Turbines on the other hand operate under favourable pressure gradients.

• Several stages of an axial compressor can be driven by a single turbine stage.

• Careful design of the compressor blading is essential to minimize losses as well as to ensure stable operation.

• Some compressors also have inlet Guide Vanes (IGV) that permit the flow entering the first stage to vary under off-design conditions.


Lect-14

Velocity triangles• Elementary analysis of axial compressors 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 Caand the tangential components will be denoted by subscript w (for eg, Cw or Vw)

• α denotes the angle between the absolute velocity with the axial direction and β the corresponding angle for the relative velocity.


Lect-14

Velocity triangles

U

C1C2

C3V1 V2

V2

C2

Rotor Stator

1 2 3

β1

β2

α2

α3

U

V1

VUC

+=


Lect-14

Velocity triangles

U

C1

C2

Ca

V1

V2

β1

β2α2

α1

ΔCw

Vw2

Vw1

Cw2

Cw1


Lect-14

Property changes across a stage

Total enthalpy

Absolute velocity

Static pressure

C1 C2 C3

h01 h02 h03

P1 P2 P3

Rotor Stator


Lect-14

Work and compression• Assuming Ca=Ca1=Ca2, from the velocity

triangles, we can see that

• By considering the change in angular momentum of the air passing through the rotor, work done per unit mass flow is

2211 tantanandtantan βαβα +=+=aa C

UCU

( )

ly.respective rotor, after the and before velocity fluid theof components

l tangentia theare and where, 2112 wwww CCCCUw −=


Lect-14

Work and compression

w

a

a

CUwUCw

UCw

∆=−=∴

−=−−=

s,other wordIn )tan(tan

)tan(tan)tan(tan,Since)tan(tan

as, written be alsocan equation above The

21

2112

12

ββββαα

αα

• The input energy will reveal itself in the form of rise in stagnation temperature of the air.

• The work done as given above will also be equal to the change in stagnation enthalpy across the stage.


Lect-14


01

0st

01

03

0103

0103st

st

0203

0101

00102

0102

1

as expressed becan This

as ,,efficiency stage define usLet stator, he through tpasses fluid the

as done is work no and adiabatic is flow theSince

TT

TT

hhhh

TT

TcCU

TT

cCUTT

CUhh

s

s

p

w

p

w

w

∆+=

−−

=

=

∆=

∆⇒

∆=−

∆=−

η

η

η


Lect-14


( )

( )1/

0101

03

1/

01

0

01

03

01030

1

give, oequation tearlier with thecombined becan This

1

ratio, pressure of In terms equation, above In the

−

−

∆+=

∆+=

−=

γγ

γγ

η

η

TcCU

PP

TT

PP

TTΔT

p

wst

st


Lect-14

Work and compression• From the above equation that relates the

per stage temperature rise to the pressure ratio, it can be seen that to obtain a high temperature ratio for a given overall pressure ratio (for minimizing number of stages),– High blade speed: limited by blades stresses– High axial velocity, high fluid deflection

(β1-β2): Aerodynamic considerations and adverse pressure gradients limit the above.


Lect-14

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


Lect-14

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.


Lect-14

Degree of reaction

( )

( )

0102

12

0102

12

01030103

1212

0102

12

0103

12

1 stage, for the and

rotor for the1 flow, ibleincompressnearly aFor

stage in the riseenthalpy Stagnationrotor in the riseenthalpy Static

PPPP

hhhhR

PPhh

PPhh

hhhh

hhhh

R

x

x

−−

≅−−

=∴

−≅−

−≅−

−−

≈−−

=

=

ρ

ρ


Lect-14

Degree of reaction

)tan(tan2

or,

)tan(tan22

1 tion,simplificaOn

And, velocity,axialconstant For

)(2

22

equation,energy flowsteady theFrom

21

21

2121

22

21

22

21

12

22

21

0103

12

22

2

21

1

ββ

βα

+=

−−=

−=−−=−

−−

=−−

=∴

+=+

UCR

UCR

CCVVVVVV

CCUVV

hhhhR

VhVh

ax

ax

wwww

ww

wwx


Lect-14

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 −=


Lect-14

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


Lect-14

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 at the velocity theis and edge trailingat the velocity ideal theis andpoint pressure minimum the

at velocity surface ideal theis Where,

1

2

max1

2max

VV

VV

VVD −=∗


Lect-14

Diffusion factor

0 50 100

V2

V1

Vmax

Suction surface

Pressure surface

Velo

city

Percent chord


Lect-14

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. ebetween thspacing theis and blade theof chord theis Where,

21

1

21

1

2

sC

VsC

VVVVD ww

−

+−=∗


Lect-14

In this lecture...• Axial flow compressors

– Basic operation of axial compressors– Velocity triangles– Work and compression– Design parameters

• Flow coefficient• Loading coefficient• Degree of reaction• Diffusion factor


Lect-14

In the next lecture...

• Cascade analysis– Cascade nomenclature– Loss and blade performance estimation

lect-14 · basic operation of axial compressors • turbines on the other hand operate under...

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