1

Lect-18

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

Lect-18

In this lecture...

• Elements of centrifugal compressors

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay3

Lect-18

Centrifugal compressors

• Centrifugal compressors were used in the first jet engines developed independently by Frank Whittle and Hans Ohain.

• Centrifugal compressors still find use in smaller gas turbine engines.

• For larger engines, axial compressors need lesser frontal area and are more efficient.

• Centrifugal compressors can develop higher per stage pressure ratios.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay4

Lect-18

Centrifugal compressors stage

Schematic of a typical centrifugal compressor

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay5

Lect-18

Centrifugal compressors stage

Typical centrifugal compressor rotors

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay6

Lect-18

Centrifugal compressor stage

[ ]

[ ]

22)()(,

22

equation,energy flowsteady theFrom in which,)()(,

)()(/, thereforeis massunit per work totalThe

ly.respective outlet, andinlet compressor thedenotes 2 and 1 where,)()(

rotor by the fluid on the applied torqueThe

21

22

1212

21

22

120102

12

12

12

CCUCUChhor

CChhhhw

ΩrUUCUCworrCrCΩmΩw

rCrCm

ww

ww

ww

ww

+−−=−

−+−=−=

=−=−==

−=

τ

τ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay7

Lect-18

Centrifugal compressor stage

r1

r2

b U2

U1

Ω

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay8

Lect-18

Centrifugal compressor stage

−

Ω=

−−

Ω=

−=

−

Ω=

−−−=−

22 flow, isentropican For

22

/,22

.,.

2222

to,ed transformgetsequation above The

222

222

222

21

22

21

22

12

VdrddP

TdsdVrddP

dPdhTdsSince

dVrddhei

VVUUhh

ρ

ρ

ρ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay9

Lect-18

Centrifugal compressor 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.

)2/(/ 2VddP −=ρ

0)2/( 22 >Ω rd

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay10

Lect-18

Centrifugal compressor stage

• However most centrifugal compressors do have deceleration and hence are liable to boundary layer separation,

• Centrifugal compressor rotor is not essentially limited by separation the way axial compressor is.

• It is therefore possible to obtain higher per stage pressure rise from a centrifugal compressor as compared to axial flow compressors.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay11

Lect-18

Impeller

• In principle, there are three possibilities for a centrifugal compressor rotor.– Straight radial– Forward leaning– Backward leaning

• Forward leaning blades are not used due inherent dynamic instability.

• Straight and backward leaning blades are commonly used in modern centrifugal compressor rotors.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay12

Lect-18

Impeller

U2

C2

V2

U2

C2

V2

U2

C2V2β2 β2

β2β2

Ω ΩΩ

Forward leaning blades(β2 is negative)

Straight radial Backward leaning blades(β2 is positive)

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay13

Lect-18

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.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay14

Lect-18

Inducer

rt rm rh

V’t

m m

U1

V1

C1β2

Inducer

Section m-m

Ut Um Uh

Ct

βhβm

βt

Leading edge velocity triangles

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay15

Lect-18

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,

outlet.inducer at the velocity relative thedenotes Where,

cos 11'

'ttt

VVV β=

1' VV <

trel MM 111 cos/ β=

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay16

Lect-18

Coriolis acceleration

• We have discussed earlier that pressure change due to the centrifugal force field is not a cause of boundary layer separation.

• This can also be explained by the Coriolisforces that are present in centrifugal compressor rotors.

• Let us consider a fluid element travelling radially outward in the passage of a rotor.

• We shall examine the velocity triangles of this fluid during a time period dt.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay17

Lect-18

Coriolis acceleration

Ωr

V

Ω

Ωdr VdθdCw

dC Vdθ

CC’Ωr

Ω(r+dr)

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay18

Lect-18

Coriolis acceleration

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

VPr

VadtVVdtdVor

VddrdV

w

w

Ω−=∂∂

Ω=Ω+Ω=

+Ω=

ρθ

θ

θ

21 magnitude, ofdirection

l tangentiain thegradient pressure a requiresit and2 ,on accelerati Coriolis theThus,

,,

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay19

Lect-18

Coriolis acceleration

• The existence of the tangential pressure gradient means that there will be a positive gradient of V in the tangential direction.

• This means that there will be a tangential variation in relative velocity.

( )

Ω=

−=−=

21,Therefore

2/1 2

θ

θθθρ

ddV

r

ddV

rV

rdVd

rddP

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay20

Lect-18

Slip factor

• Towards the outlet of the impeller, as the Coriolis pressure gradient disappears, there will be a difference between Vw2 and U2.

• 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.

22 /UVws =σ

Ns /21−≈σ

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay21

Lect-18

Coriolis acceleration

V

Cw2

C2V2U2

Straight radial blades

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay22

Lect-18

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.

• The fluid flows radially outwards from the impeller, through a vaneless region and then through a vaned diffuser.

• Both vaned and the vaneless diffusers are controlled by boundary layer behaviour.

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay23

Lect-18

The diffuser

Ω

r3

r2

r1

r3>r2>r1

Diffuser vanes

Vaneless space

Impeller

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay24

Lect-18

The diffuserRad

ial d

irec

tion

Cr

CW

Cα

Streamlines in a radial diffuser

Logarithmic spiral

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay25

Lect-18

The diffuser

space. vanelessin the place takingdiffusion is that there means This radius. toalproportioninversely is velocity theThus,

direction. radial theandvelocity ebetween th angle theis where,tanconstant

constantmomentum,angular ofon conservati From

constant.)2( ,continuity From width.axialconstant

ofregion vanelessain flow ibleincompressan consider usLet

αα

πρ

==∴=

==

rw

w

r

/CCrC

Crhm

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay26

Lect-18

In this lecture...

• Elements of centrifugal compressors

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay27

Lect-18

In the next lecture...

• Performance characteristics of centrifugal compressors

• Surging and choking