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In this lecture...

• Centrifugal compressors
  • Coriolis acceleration
  • Slip factor
  • Performance characteristics
  • Stall and surge

Ωr

V

Ω

Ωdr (^) Vdθ

dC (^) w

dC V C’^ C dθ Ωr Ω(r+dr)

Coriolis acceleration

Coriolis acceleration

• The magnitude of the relative velocity is unchanged, but the particle has suffered an absolute change of velocity.

P V r

direction of magnitude,

andit requires apressure gradient in the tangential

Thus, the Coriolis acceleration, a V

or, dC Vdt V dt,

dC dr Vd w

w

ρ Ω θ

Ω

Ω Ω

Ω θ

θ

(^12)

2

= − ∂

∂

=

= +

= +

Coriolis acceleration

V

C (^) w

C (^2) U 2 V^2

Straight radial blades

Slip factor

• Towards the outlet of the impeller, as the Coriolis pressure gradient disappears, there will be a difference between C (^) w2 and U 2.
• This difference in the velocities is expressed as slip factor,
• The slip factor is approximately related to the number of blades of the impeller.
• For a straight radial blade, the slip factor is empirically expressed as , where N is the number of blades.

σs = C (^) w 2 /U 2

σs ≈ 1 − 2 / N

Performance characteristics

• The centrifugal compressor performance characteristics can be derived in the same way as an axial compressor.
• Performance is evaluated based on the dependence of pressure ratio and efficiency on the mass flow at different operating speeds.
• Centrifugal compressors also suffer from instability problems like surge and rotating stall.

Performance characteristics

• The compressor outlet pressure, P 02 , and the isentropic efficiency, ηC, depend upon several physical variables



 

 

 





 

 

 



=

(^0101)

01 01

02

2

01

2 01

01 01

02

02 01 01

T

N , P

m T , f P

P The above reduces to

, ,design D , RT

D , P D

m RT , f P

P

In terms of non - dimensionless parameters,

P , f(m,P ,T , , ,R, ,design,D)

C

C

C







η

γ ν

Ω γ

γ Ω η

η Ω γ ν

Performance characteristics

Mass flow

Pressure ratio

A

B

C

D

E

Constant speed line

Choking limit

Surging limit

Performance characteristics

01

02 P

P

δ

m  θ

θ

N

Surge line Locus of points of maximum efficiency

Performance characteristics

• There are two limits to the operation of the compressor.
• Operation between A and B are limited due to occurrence of surge.
• Surging: sudden drop in delivery pressure and violent aerodynamic pulsations.
• Operation on the positive slope of the performance characteristics: unstable
• Surging usually starts to occur in the diffuser passages.

Performance characteristics

• The pressure ratio or the temperature rise in a centrifugal compressor also depends upon the blade shaping.
• There are three possible types of blade shapes: forward leaning, straight radial and backward leaning.
• Theoretically, the forward leaning blading produces higher pressure ratio for a given flow coefficient.
• However such a blading has inherent dynamic instability.
• Therefore, straight radial or backward leaning blades are popularly used.

Rotating stall

• Rotating stall might also affect the compressor performance.
• In this case a stall cell (that might cover one or more adjacent blades) rotates within the annulus.
• Full annulus rotating stall may eventually lead to surge.
• Rotating stall may also lead to aerodynamically induced vibrations and fatigue failure of the compressor components.

Rotating stall

Propagation of rotating stall