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In this lecture...

• Centrifugal compressors
  • Thermodynamics of centrifugal compressors
  • Components of a centrifugal compressor

Centrifugal compressors

• Besides small aero engines, centrifugal compressors are used in the auxiliary power units (APUs) in many aircraft.
• Some of the aircraft air conditioning systems employ centrifugal compressors.
• In a few engines, centrifugal compressors are used as the final stage of the compression process downstream of a multi-stage axial compressor. Eg. GE T 700, P&W PT6, Honeywell T53.

Centrifugal compressors stage

Typical centrifugal compressor rotors

Centrifugal compressors stage

s

T 02

01

2

03 02s

1

3 03s

P 02 P 3 P 2 P 01 P 1

c p C 2

(^23)

T-s diagram for a centrifugal compressor

P 03

c p C 2 12

c p C 2

(^22)

T 02 =T 03

T 2

T 1

T 01

Total losses Impeller losses

Centrifugal compressors stage

[ ]

[ ]

2 2

2 2 2 1 2 2 1 2 1 2

2 1 2 02 01 2 1 2

2 1

2 1

2 1

or, h h (UC ) (UC ) C^ C

w h h h h C C

From the steady flow energy equation,

or, w (UC ) (UC ) in which,U Ωr

w Ω /m Ω(rC ) (rC )

The totalwork per unit massis therefore,

compressor inlet andoutlet,respectively.

m(rC ) (rC ) ,where 1 and 2 denotes the

The torque applied on the fluidby therotor

w w

w w

w w

w w

− = − − +

= − = − + −

= − =

= = −

= −





τ

τ

Centrifugal compressors stage



 

  − 

 



 − − 

 



= −

 − 

 





 

 − = − − −

2 2

2 2

2 2

2 2 2 2

2 2 2

2 2 2

2 2 2

2 1 2 2 2 1 2 2 2 1

For anisentropic flow, dP d r d^ V

dP d r dV Tds

Since, Tds dh dP /

i.e., dh d r dV

h h U U V V

The above equation gets transformedto,

Ω ρ

Ω ρ

ρ

Ω

Centrifugal compressors stage

• For axial compressors, dr≈0 and the above equation reduces to
• Thus in an axial compressor rotor, pressure rise can be obtained only be decelerating the flow.
• In a centrifugal compressor, the term

, means that pressure rise can be obtained even without any change in the relative velocity.

• With no change in relative velocity, these rotors are not liable to flow separation.

dP /ρ = −d(V^2 / 2 )

d( Ω^2 r^2 / 2 ) > 0

Conservation of Rothalpy

• If we were to assume steady, viscous flow without heat transfer
• Here, I, is the rotational enthalpy or rothalpy.
• It is now known that rothalpy is conserved for the flow through the impeller.
• Any change in rothalpy is due to the fluid friction acting on the stationary shroud (if considered in the analysis).

U C I C U C h C h + − w = + − 2 w 2 =

2 2 1 1 2

2 1 (^1 )

Impeller

• Impeller draws in the working fluid. It is the rotating component of the centrifugal compressor.
• The diverging passages of the impeller diffuses the flow to a lower relative velocity and higher static pressure.
• Impellers may be single-sided or double- sided, shrouded or un-shrouded.
• In the impeller, the working fluid also experiences centripetal forces due to the rotation.

Impeller

U (^2) C (^2)

V (^2)

U (^2)

C (^2)

V (^2)

U (^2) β 2 C (^2) β 2 V^2

β 2 β^2 Ω (^) Ω Ω

Forward leaning blades (β 2 is negative)

Straight radial Backward leaning blades (β 2 is positive)

Inducer

• Inducer is the impeller entrance section where the tangential motion of the fluid is changed in the radial direction.
• This may occur with a little or no acceleration.
• Inducer ensures that the flow enters the impeller smoothly.
• Without inducers, the rotor operation would suffer from flow separation and high noise.

Inducer

• It can be seen from the above that
• It can be seen that , which indicates diffusion in the inducer.
• Similarly, we can see that the relative Mach number from the velocity triangle is,

inducer outlet.

Where, V denotes the relative velocity at the

V V cos '

t t

' t = 1 β 1

V V 1 ' (^) <

M 1 rel = M 1 /cosβ 1 t

The diffuser

• High impeller speed results in a high absolute Mach number leaving the impeller.
• This high velocity is reduced (with an increase in pressure) in a diffuser.
• Diffuser represents the fixed or stationary part of the compressor.
• The diffuser decelerates the flow exiting the impeller and thus reduces the absolute velocity of the working fluid.
• The amount of deceleration depends upon the efficiency of the diffusion process.