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
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