lect- 11 · • in a multi-stage compressor,a small departure from the design point at the first...

1

Lect- 11

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

Lect-11

In this lecture...

• Performance characteristics of axial flow compressors• Single stage characteristics• Multi-stage characteristics


Lect-11

Single stage performance characteristics

• Let us consider a typical axial compressor stage comprising of a set of rotor blades followed by a set of stator blades.

U

C1C2

V1 V2

Rotor Stator

U

C3

α3


Lect-11


U

C1

C2

Ca

V1

V2

β1

β2α2

α1

ΔCw

Vw2

Vw1

Cw2

Cw1


Lect-11


• From the above velocity triangles,

( )[ ]

( )2120

210

0

122

tantan1,

tantan Since,

tantan

βα

βα

αβ

+−==∆

+−=∆=

=−=

UC

UΔh

UCor

CUUΔhCUΔh

CCandCUC

aw

a

w

awaw


Lect-11


• Change in the design mass flow rate affects Ca, change in rotor speed affects U.

• Change of either Ca or U changes the inlet angle β1 at which the flow approaches the rotor.

• The above equation shows that the blade performance depends upon the ratio Ca/U.

) , ,f( eperformanc Stage Thus,

.efficiency the and tcoefficien flow t,coefficien loading the of function a is eperformanc stage The

ηφψ=


Lect-11


UC

Uh w∆

=∆

20

design

UCa

design

UCa

UCa

UCa

stηMeasured

Measured

1.0

( )2120 tantan1 βα +−==

∆UC

UΔh

UC aw

( )design21 tantan βα +1

Stage loading

Stage efficiency


Lect-11


U

C1

V1

β1

V1

β1α1

Ca

design

operation Normal :conditionDesign

=

UC

UC aa

U

C1

V1

β1

V1

β1α1

Ca

U

C1

V1

β1

V1

β1α1

Ca

design

separation flow incidence Positive :conditiondesign -Off

<

UC

UC aa

design

separation flow incidence Negative :conditiondesign -Off

>

UC

UC aa


Lect-11

Multi-stage performance characteristics

• Let us know consider a multi-stage compressor. Inlet station is denoted by 1 and exit of the compressor by 2.

• Therefore the overall pressure ratio of the compressor is P02/P01.

• The compressor outlet pressure, P02, and the isentropic efficiency, ηC, depend upon several physical variables


Lect-11


=

ΩΩ=

Ω=

0101

01

01

02

2

012

01

01

01

02

010102

,,

toreduces above theTherefore fixed. are and Also, tly.significan eperformanc affect thenot do and that assumecan wedesign,given aFor

design,,,,,

,parameters essdimensionl-non of In termsdesign,,,,,,,,(,

TN

PTm

fPP

RD

DRTD

DPRTm

fPP

D)RTPmfP

C

C

C

η

νγ

γνγ

γη

νγη


Lect-11


( ) ( )( ) ( ) kPaPandKT

PP

TT

NmfPP

C

325.10115.288

andWhere,

,,

re. temperatuand pressureday standard theof in terms processedfurther is thisUsually,

day Std.01day Std.01

day Std.01

01

day Std.01

01

01

02

==

==

=

δθ

θδθη


Lect-11


01

02

PP

δθm

η


Lect-11


η

01

02

PP

δθm


Lect-11

Multi-stage performance characteristicsMulti-stage performance characteristics

• In a multi-stage compressor, a small departure from the design point at the first stage causes progressively increasing departure from design conditions from the first stage onwards.

• Thus, a small reduction in (ca/U)design at the first stage could lead to positive incidence separation at the last stage.

• Similarly, a small increase in (ca/U)design could lead to negative incidence separation in the last stage.

• The most extreme mismatching of the front and rear stages occur during starting.


Lect-11


U

C1

C2

Ca

V1

V2

β1

β2α2

α1

U

C1

C2

Ca

V1

V2

β1

β2α2

α1

Design velocity triangles

First stages Last stages


Lect-11


• Decreased Ca with α1 and β2 constant, results in increased α2 and β1 or increased loading on both rotor and stator blades.

• In the case of increased Ca, it results in the opposite effect.

• Designers use several solutions to allow compressors to self-start: use of bleed valves allowing some of the incoming air to escape, variable IGVs, multi-spooling.


Lect-11


• Axial compressors suffer from two possible modes of unstable operation– Rotating stall: non-axisymmetric, aperiodic – Surge: axisymmetric, periodic

• Rotating stall: progression around the blade annulus of a stall pattern, in which one or more adjacent blade passages are instantaneously stalled, then are cleared for unstalled flow as the stall cell progresses.

• Rotating stall causes alternate loading and unloading of the blades: fatigue failure.


Lect-11


01

02

PP

δθm


Lect-11


Stage characteristicsThrottle characteristics

UCa

20

UP

ρ∆


Lect-11

In this lecture...

• Performance characteristics of axial flow compressors• Single stage characteristics• Multi-stage characteristics

lect- 11 · • in a multi-stage compressor,a small departure from the design point at the first...

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