Analysis of Performance Characteristics: Axial Flow Compressors, Slides of Turbomachinery

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1

In this lecture...

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

Single stage performance characteristics

U

C (^1)

C (^2)

C (^) a

V 1

V 2

β 1

α^ β^2 2

α 1

ΔC (^) w

Vw Vw

C (^) w

C (^) w

Single stage performance characteristics

• From the above velocity triangles,

[ ( )]

20 (^12 )

0 1 2

0

2 2 1

, 1 tan tan

tan tan

Since,

tan tan

α β

α β

β α

U

C

U

Δh

U

C

or

Δh U U C

Δh U C

C U C and C C

w a

a

w

w a w a

Single stage performance characteristics

U

C U

∆ h 20 (^) =∆ w

 design   

 U

C (^) a

 design   

 U

C (^) a

 C U^ a 

 C U^ a 

η (^) st Measured

Measured

∆ UC (^) w = U Δh 20 = 1 − C Ua ( tanα + 1 tan β 2 )

( tanα + 1 tan β 2 )design

1

Stage loading

Stage efficiency

Single stage performance characteristics

U C (^1)

V (^1)

β 1

V (^1)

β 1 α 1 C (^) a

design

Normaloperation

Designcondition:

 CU^ a = C Ua 

U C (^1)

V (^1)

β 1

V (^1)

β 1 α 1 C (^) a

U C (^1)

V (^1)

β 1

V (^1)

β 1 α 1 C (^) a

design

Positiveincidenceflowseparation

Off-designcondition:

 CU^ a < C Ua  design

Negativeincidenceflowseparation

Off-designcondition:

 CU^ a > C Ua 

Multi-stage performance characteristics

(^0101)

01 01

02

2

01

2 01

01 01

02

02 01 01

arefixed.Thereforethe abovereduces to

affect theperformancesignificantly.Also, and

For a givendesign, wecanassume that and do not

, , , , ,design

In termsof non-dimensionless parameters,

, ( , , , , , , ,design,

T

N

P

m T f P

P

D R

D

RT

D

P D

m RT f P

P

P f m P T R D)

C

C

C

η

γ ν

γ γ ν

γ η

η γ ν

Multi-stage performance characteristics

( ) ( ) ( T ) K and ( P ) kPa

P

P

T

T

m N f P

P

C

Where, and

standardday pressureand temperature.

Usually,this isfurther processedin termsof the

(^01) Std.day (^01) Std.day

(^01) Std.day

01 (^01) Std.day

01

01

02

θ δ

δ θ

θ η

Multi-stage performance characteristics

η

01

02 P

P

δ

m  θ

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.

Multi-stage performance characteristicsMulti-stage performance characteristics

• Decreased C (^) a with α 1 and β 2 constant, results in increased α 2 and β 1 or increased loading on both rotor and stator blades.
• In the case of increased C (^) a , 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.

Multi-stage performance characteristicsMulti-stage performance characteristics

• 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.

Multi-stage performance characteristicsMulti-stage performance characteristics

Stage characteristics Throttle characteristics

U

C (^) a

U^02

P ρ

∆

In this lecture...

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