2. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
tip2β
tip1β
Previous discussion covers the theory behind the
calculation of rotor and stator angles at mean
radius.
Further study on previous theory enables
compressor designer to evaluate the change of
angles from root section up to tip section of rotor
and stator (covering all stages in axial compressor).
root1β
root2β
2Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
Variation of rotor angles from root to tip section
3. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Cw
dr
( )[ ]
( )[ ] ( )d
rdrr
d
Area
c
c
−+××=
≈θ
π
π
θ
2
22
2
2
dr
r ( )[ ] ( )
drrdrdrrdrr
d cdr
c
×× →−×++× ≈
θ
θ 0222 2
2
2
ar
Note: unit width element
r
CA
r
CV
r
Cm
FforcelCentrifuga www
cw
×××
=
××
=
×
==
ρρ 222
1
_
( ) drdC
r
drrdC
rrr
c
w
c
w
×××=
××××
θρ
θρ 2
2
a
r
3Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
4. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
dPP +
( ) ( )
c
d
rdrdPPF
θ
π ××××+×+= 12
dP
P +2
dP
P +
( ) ( )
( ) ( ) c
topradial
drdrdPP
d
rdrdPPF
θ
π
θ
π
×+×+
×
×
×××+×+=
a
1
2
2,
2
P +2
P +
P
c
bottomradial drPF θ××=,
c
sideradial
d
dr
dP
PF
θ
××
+×=
2
sin
2
2,
c
c
dPddP
θ
θ
××
+=××
+×
22
Since dθθθθ very small, 22
sin
cc
dd θθ
≈
c
ddr
dP
P
d
dr
dP
P θ
θ
××
+=××
+×
222
2a
4Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
5. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
dPP +
dP
P +2
dP
P +
2
P +2
P +
P
( ) ( ) ccc
ddr
dP
PdrPdrdrdPPF θθθ ××
+−××−×+×+= ( ) ( )
( )c
c
ccc
netradial
drdP
ddrdP
ddr
dP
PdrPdrdrdPPF
θ
θ
θθθ
××+
××
××
+−××−×+×+=
2
,
a ( )c
drdP θ××+
2
a
5Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
6. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
netradialcw FF ,=
( )drdP
ddrdP
drdC c
c
c
w
2
××+
××
=××× θ
θ
θρ ( )
r
dr
ddPdrdC
drdPdrdC
cc
w
w
2
2
2
+××=×××
××+=×××
θθρ
θθρ
a
r
dr
d
Cd
dr
dP
c
w
c 2
2
+×
××
=
θ
θρ
a
r
C
dr
Cd
dr
dP
rd
w
dr
w
c 2
0
2
2
1
2
→
×
=×
+×
≈θ
ρ
θ
a
r
r
dr
d
dr c
2
→
+×
=×
θ
ρ
a
r
C
dr
dP w
2
1
=×
ρ
Radial equilibrium equation:
6Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
7. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
PdvvdPdudh
Pvuh
++=
+=
a
Enthalpy Gibbs equation
( ) PdvPdvvdPdhTds
PdvduTds
+−−=
+=
a
PdvvdPdhdu
PdvvdPdudh
−−=
++=
a
a ( )
dP
dhTds
vdPdhTds
PdvPdvvdPdhTds
ρ
−=
−=
+−−=
a
a
a
ddPdTdsdh
dP
Tdsdh
ρ
ρ
ρ
11
+=a
dP
dr
d
dr
dP
dr
dT
ds
dr
ds
T
dr
dh ρ
ρρ 2
11
−++=a
dPdsdh 1
Dropping second order terms
dr
dP
dr
ds
T
dr
dh
ρ
1
+=
7Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
8. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Stagnation Enthalpy
C
hh +=
2
0
2
[ ]CChh
hh
wa +×+=
+=
22
0
0
2
1
2
a
dr
dC
C
dr
dC
C
dr
dh
dr
dh w
w
a
a ++=0
2
a
dPdsdh 1 CdP
2
1
dCdCdPdsdh 1
dr
dP
dr
ds
T
dr
dh
ρ
1
+=Knowing:
r
C
dr
dP w
2
1
=×
ρ
and
dr
dC
C
dr
dC
C
dr
dP
dr
ds
T
dr
dh w
w
a
a +++=0 1
a
ρ
Dropping entropy gradient yields:
dr
dC
C
dr
dC
C
r
C
dr
dh w
w
a
a
w
++=
2
0
a
Vortex energy
equation:
8Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
drdrrdr
9. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Apart from regions near the walls of the annulus^, the stagnation enthalpy (and
temperature) will be uniform across the annulus at entry to the compressor.temperature) will be uniform across the annulus at entry to the compressor.
If the frequently used design condition of constant specific work at all radii is
applied, then although h0 will increase progressively through the compressor inapplied, then although h0 will increase progressively through the compressor in
the axial direction, its radial distribution will remain uniform. Thus dh0/dr = 0 in
any plane between pair of blade rows.
dr
dC
C
dr
dC
C
r
C w
w
a
a
w
++=
2
0Constant specific work at all radii:
drdrr
^ due to the adverse pressure gradient in compressors, the boundary layers along the annulus walls thicken
as the flow progresses.
9Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
10. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
dr
dC
C
dr
dC
C
r
C w
w
a
a
w
++=
2
0
When considering possible sets of design conditions, it is usually desirable to retain the constant
specific work-input condition to provide constant stage pressure ratio up to the blade height. It would be
possible, however, to choose a variation of one of the other variables, say Cw, and determine the variation
of Ca. The radial equilibrium requirement would still be satisfied.
In this note, we use the normal design condition:
(a) Constant specific work input at all radii
(b) An arbitrary whirl velocity distribution which is compatible with (a)
To obtain constant work input, U(C - C ) must remain constant across the annulus. Let us considerTo obtain constant work input, U(Cw2 - Cw1) must remain constant across the annulus. Let us consider
distributions of whirl velocity at inlet and outlet from the rotor blade given by:
R
b
aRC n
w −=1 _2 :
r
r
Rwhere
R
b
aRC n
w =+= Kand
Check whether Cw1 and Cw2 satisfy Uλλλλ(Cw2 - Cw1)Check whether Cw1 and Cw2 satisfy Uλλλλ(Cw2 - Cw1)
R
b
CC
R
b
aR
R
b
aRCC
ww
nn
ww
_
12
12
2
λλ
=−
−−
+=−
a==
==
N
r
U
srevNwhererNU
π
π
2
/:,2
a constant “It means metal speed at any
specified radius divided by its
radius is a constant value.”
( )
r
rUb
R
Ub
CCU ww
_
12
22 λλ
λ ==−∴
radius is a constant value.”
U
rU
r
U
r
U
__
_
_
=
=
a
( )
_
Conclusion
“This is independent of radius,
10Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
r
rU =a
( )
_
12 2 UbCCU ww λλ =−
“This is independent of radius,
means the two design
conditions (a) and (b) are
therefore compatible.”
11. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
dr
dC
C
dr
dC
C
r
C w
w
a
a
w
++=
2
0Constant specific work at all radii:
drdrr
waConstant specific work at all radii:
dr
C
dCCdCC w
2
0=++
dr
C
dCCdCC
dr
r
C
dCCdCC
w
w
wwaa
2
0
+=−
=++
a
Times both side by “dr”
dr
r
C
dCCdCC w
wwaa +=−a
In terms of dimensionless R
Re-arranging
dR
R
C
dCCdCC w
wwaa
2
+=−Note: _
r
r
R =
R
11Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
12. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = 1 (first power condition)
R
b
aRC
R
b
aRC ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor exit:
[ ] [ ] dR
R
ab
R
b
Ra
CC
R
R
w
R
a
2
2
1
2
1
1
2
2
22
1
2
1
2
2
++
+=− ∫
dR
R
ab
R
b
Raab
R
b
RaCC
RR
aa
2
2
2
1
2
1
1
3
2
2
1
2
2
22
2_
2
2
2
+++
++=
−−
∫a
babRab
Rab
R
bRa
abbaab
R
b
RaCC
R
aa
11
ln2
22
22
2
1
2
1
2222222
1
2
222
22
2
2
22
2_
2
2
2
11
+−+
−−−++=
−−
a
( )RabaRaCC
ba
Rab
R
bRa
ba
R
b
RaCC aa
ln22
0
22
ln2
222
1
2
1
222
2_
2
22
2
222
22
2
2
22
2_
2
2
2
+−−=−∴
−+−+−+
−−+=
−−a
12Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
( )RabaRaCC aa ln22 222
2
2
2 +−−=−∴
13. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = 1 (first power condition)
R
b
aRC
R
b
aRC ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor inlet:
[ ] [ ] dR
R
ab
R
b
Ra
CC
R
R
w
R
a
2
2
1
2
1
1
2
2
22
1
2
1
2
1
−+
+=− ∫
dR
R
ab
R
b
Raab
R
b
RaCC
RR
aa
2
2
2
1
2
1
1
3
2
2
1
2
2
22
2_
1
2
1
−++
−+=
−−
∫a
babRab
Rab
R
bRa
abbaab
R
b
RaCC
R
aa
11
ln2
22
22
2
1
2
1
2222222
1
2
222
22
2
2
22
2_
1
2
1
11
−−+
+−−−+=
−−
a
( )RabaRaCC
ba
Rab
R
bRa
ba
R
b
RaCC aa
ln22
0
22
ln2
222
1
2
1
222
2_
2
22
2
222
22
2
2
22
2_
1
2
1
−−−=−∴
++−−−+
−−+=
−−a
13Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
( )RabaRaCC aa ln22 222
1
2
1 −−−=−∴
14. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = 0 (exponential condition)
R
b
aC
R
b
aC ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor exit:
+++
++=
−− ∫ dR
R
ab
R
b
R
a
R
ab
R
b
aCC
RR
aa
22
2
1
2
1
1
23
22
1
2
2
2
2_
2
2
2
−−+
−−−++=
−−
∫
R
ab
R
b
Raabba
R
ab
R
b
aCC
RRRRR
R
aa
2
2
ln2
2
2
1
2
1
22
1
2
2
222
2
2
2
2_
2
2
2
11
a
++−−−+
−−+=
−−
ab
b
R
ab
R
b
Raabb
R
ab
R
b
CC
RRRR
aa 2
2
0
2
2
ln2
2
2
1
2
1
222
2
2
2
22
2
22_
2
2
2
1
a
−+−=−∴
R
ab
RaabCC aa ln2 2
2_
2
2
2
14Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
15. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = 0 (exponential condition)
R
b
aC
R
b
aC ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor inlet:
−++
−+=
−− ∫ dR
R
ab
R
b
R
a
R
ab
R
b
aCC
RR
aa
22
2
1
2
1
1
23
22
2
2
2
2_
1
2
1
+−+
+−−−+=
−−
∫
R
ab
R
b
Raabba
R
ab
R
b
aCC
RRRRR
R
aa
2
2
ln2
2
2
1
2
1
22
1
2
2
222
2
2
2
2_
1
2
1
11
a
−+−+−+
+−−=
−−
ab
b
R
ab
R
b
Raabb
R
ab
R
b
CC
RRRR
aa 2
2
0
2
2
ln2
2
2
1
2
1
222
2
2
2
22
2
22_
1
2
1
1
a
++−−=−∴
R
ab
RaabCC aa ln2 2
2_
1
2
1
15Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
16. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = -1 (free vortex condition)
R
b
R
a
C
R
b
R
a
C ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor exit:
33
2
3
2
22
2
2
22_
2
2
2
2211
RR
aa dR
abbaabba
CC
+++
++=
−− ∫
22
2
2
2
22
22
2
2
22_
2
2
2
1
333
1
22222
2
2
22
2
2
2
1
2
1
22
R
aa
aa
R
ab
R
b
R
a
abba
R
ab
R
b
R
a
CC
dR
RRRRRR
CC
−−−+
−−−++=
−−
+++
++=
−− ∫
a
22
22
2
2
2
22
22
2
2
22_
2
2
2
1
222
2
22
2
2
2
1
2
1
22222
aa ab
ba
R
ab
R
b
R
a
abba
R
ab
R
b
R
a
CC
RRRRRR
+++−−−+
−−−++=
−−
a
2_
2
2
2 aa CC =∴
16Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
17. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
When n = -1 (free vortex condition)
R
b
R
a
C
R
b
R
a
C ww +=−= 21 ,
dR
R
C
dCCdCC w
wwaa
2
+=−
For rotor inlet:
33
2
3
2
22
2
2
22_
1
2
1
2211
RR
aa dR
abbaabba
CC
−++
−+=
−− ∫
22
2
2
2
22
22
2
2
22_
1
2
1
1
333
1
22211
2
2
22
2
2
2
1
2
1
22
R
aa
aa
R
ab
R
b
R
a
abba
R
ab
R
b
R
a
CC
dR
RRRRRR
CC
+−−+
+−−−+=
−−
−++
−+=
−− ∫
a
22
22
2
2
2
22
22
2
2
22_
1
2
1
1
222
2
22
2
2
2
1
2
1
22222
aa ab
ba
R
ab
R
b
R
a
abba
R
ab
R
b
R
a
CC
RRRRRR
−+++−−+
+−−−+=
−−
a
2_
1
2
1 aa CC =∴
17Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
18. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Degree of Reaction (DOR), ΛΛΛΛ provides a measure of the extent to which the rotor contributes to theDegree of Reaction (DOR), ΛΛΛΛ provides a measure of the extent to which the rotor contributes to the
overall static pressure rise in the stage. It is defined as:
ΛΛΛΛ =
Static enthalpy rise in the rotor
Static enthalpy rise in the stage
Steady flow energy equation:
( ) ( )1 2222
−+−+−
∆
=Λ
CCUCCCC
W
TC rotorp
( )12 ww CCUW −=
Since all the work input to the stage takes
Steady flow energy equation:
( ) ( )
( )
( ) 1
2
1
2
2
2
1
2
2
2
1
12
12
2
2
2
1
2
2
2
1
+
−+−
=Λ
−
−+−+−
=Λ
CCCC
CCU
CCUCCCC
awwa
ww
wwawwa
a
Since all the work input to the stage takes
place in the rotor, the steady flow energy
equation yields:
( )
( )
( )
( )
( )
( )
1
22
1
2
2
2
2
1
2
2
2
1
12
2121
+
−
−
+
−
−
=Λ
+
−
−+−
=Λ
CCU
CC
CCU
CC
CCU
CCCC
wwaa
ww
awwa
a
a
( )221
CCTCW −+∆= ( ) ( )
( )
( )
( )( )
( )
( ) ( )( )
1
22
22
12
2121
12
2
2
2
1
1212
+
−
−+
+
−
−
=Λ
−−
CCU
CCCC
CCU
CC
CCUCCU
ww
wwww
ww
aa
wwww
a
( )
( ) ( )
( ) ( )22
12
2
1
2
2
2
1
2
2
1
2
1
:
2
wwrotorp
rotorp
CCUCCTC
CCUCCTCHence
CCTCW
−+−=∆
−=−+∆
−+∆=
( )
( )
( )( )
( )
( ) ( )
1
22
22
12
1221
12
2
2
2
1
+
+
−
−
=Λ∴
+
−
−+
−
−
−
=Λ
CCCC
CCU
CCCC
CCU
CC
ww
wwww
ww
aa
a
( ) ( )
( ) ( )12
2
2
2
2
2
1
2
1
12
2
2
2
1
2
1
2
1
wwwawarotorp
wwrotorp
CCUCCCCTC
CCUCCTC
−+−−+=∆
−+−=∆
a
a
18Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
( )
( )
( ) 1
22
21
12
21
+
+
−
−
−
=Λ∴
U
CC
CCU
CC ww
ww
aa
19. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
First power, n = 1First power, n = 1
( )RabaRaCC aa ln22 222
2_
1
2
1 −−−=
( )RabaRaCC ln22 222
2_
2
+−−=
( ) ( )RabaRaCRabaRaCCC aaaa ln22ln22 2222
2
_
2222
1
_
2
2
2
1 +−+−−−−=−
( )RabaRaCC aa ln22 222
2
2
2 +−−=
2_
2
2_
1 aa CC =
RabCC aa ln8
2
2
2
1 =−∴
b
aRC −=
R
b
aRCw −=1
R
b
aRCw +=2
R
b
R
b
aR
R
b
aRCC ww 212 =
−−
+=− aR
R
b
aR
R
b
aRCC ww 212 =
−+
+=+and
ln22ln8
aRRaRaRRab
R
1:
1
ln2
1
2
2
22
ln8
=
+
−
=+
−
=Λ
RWhen
U
aR
U
RaR
U
aR
R
b
U
Rab
( )
( )
( ) 1
22
21
12
2
2
2
1
+
+
−
−
−
=Λ
U
CC
CCU
CC ww
ww
aa
111
1:
____
___
__
_
Λ−=⇒Λ−=⇒−=Λ
=
Ua
U
a
U
a
RWhen( ) 22 12 − UCCU ww
U
R
U
RUU
r
U
r
U
Note =⇒=⇒= _
_
_
_
1
:
11ln121
1ln12 __
_
__
_
__
+
Λ−−
Λ−⇒+
Λ−
−
Λ−
=Λ R
RU
RU
RU
RRU
19Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
UUrr
( ) 11ln21
_
+−
Λ−=Λ∴
R
20. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Exponential, n = 0Exponential, n = 0
++−−=
R
ab
RaabCC aa ln2 2
2_
1
2
1
−+−=
ab
RaabCC ln2 2
2_
2
−++−
++−−=−
R
ab
RaabC
R
ab
RaabCCC aaaa ln2ln2 22
2
_
22
1
_
2
2
2
1
−+−=
R
ab
RaabCC aa ln2 2
2
2
2
2_
2
2_
1 aa CC =
−=−∴
R
ab
abCC aa 4
2
2
2
1
b
andR
b
aCw −=1
R
b
aCw +=2
R
b
R
b
a
R
b
aCC ww 212 =
−−
+=− a
R
b
a
R
b
aCC ww 212 =
−+
+=+
2
4
−
−
−
aababRa
R
ab
ab
a
ab
abR
1
2
1
111
2
2
22
4
+
−
=+
−
−
=Λ
+
−
−
=+
−
−
=+
−
−
=Λ
aaRaaaR
U
a
Ub
ababR
U
a
Ub
R
R
ab
U
a
R
b
U
R
ab
a
( )
( )
( ) 1
22
21
12
2
2
2
1
+
+
−
−
−
=Λ
U
CC
CCU
CC ww
ww
aa
111
1:
11
___
__
_
Λ−=⇒Λ−=⇒−=Λ
=
+
=+
−
=Λ
Ua
U
a
U
a
RWhen
UUU
a( ) 22 12 − UCCU ww
U
R
U
RUU
r
U
r
U
Note =⇒=⇒= _
_
_
_
1
:
1
12
11
121
_
_
_
____
+
Λ−
−
Λ−⇒+
Λ−−
Λ−
=Λ
RRU
URU
UU
20Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
UUrr
1
2
11
_
+
−
Λ−=Λ∴
R
21. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Free vortex, n = -1Free vortex, n = -1
2_
1
2
1 aa CC =
2_
2
CC = 0
2
2
2
1 =− aa CC
2_
2
2_
1 aa CC =
2
2
2 aa CC = 021 =− aa CC
ba
and
R
b
R
a
Cw −=1
R
b
R
a
Cw +=2
R
b
R
b
a
a
R
b
R
a
CC ww 212 =
−−
+=−
R
a
R
b
R
a
R
b
R
a
CC ww 212 =
−+
+=+
2
a
( )
( )
( ) 1
22
21
12
2
2
2
1
+
+
−
−
−
=Λ
U
CC
CCU
CC ww
ww
aa
RR
=
+
−=+
−=+
−
=Λ
1:
1101
2
2
22
0
RWhen
UR
a
UR
a
U
R
a
R
b
U
( ) 22 12 − UCCU ww
Λ−=⇒Λ−=⇒−=Λ
=
____
___
__
_
111
1:
U
Ua
U
a
U
a
RWhen
U
R
U
RUU
r
U
r
U
Note =⇒=⇒= _
_
_
_
1
:
+
Λ−
−=+
Λ−
−=+
Λ−
−=Λ 2
____
1
1
1
1
1
1
RUR
R
U
UR
U
21Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
UUrr
Λ−−=Λ∴
_
2
1
1
1
R
22. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
( )
_
( )
_
12 2 TCUbCCUW spww λλ ∆==−=
_
TC
b
p∆
=∴ _
2 U
b
λ
=∴
Note: this is applicable for all cases (i.e. n = 1, 0 and -1)Note: this is applicable for all cases (i.e. n = 1, 0 and -1)
22Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
23. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
−CU
−
= −
a
w
C
C
CU1
tanβ
Variation of rotor and stator angles
can therefore be calculated as a
function of radius.
= −
a
w
C
C1
tanα
function of radius.
23Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
24. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
Example: RB211-24G
RB211-24G’s axial compressors at ISO conditions:
a. Pressure ratio = 20
b. Mass flow rate = 100 kg/s
c. LP axial compressor = 7 stages
24Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
c. LP axial compressor = 7 stages
d. HP axial compressor = 6 stages
25. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
25Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
26. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
26Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
beta 1
beta 2
alpha 1
alpha 2
root
tip
mean radius
a1 = alpha 1
a2 = alpha 2
b1 = beta 1
b2 = beta 2
fv = free vortex (n = -1)
exp = exponential (n = 0)
fp = first power (n = 1)
27. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
27Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
dhr = de Haller number for rotor
dhs = de Haller number for stator
fv = free vortex (n = -1)
exp = exponential (n = 0)
fp = first power (n = 1)
root mean radius tip
28. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
28Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
29. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
29Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
30. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
30Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
31. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
31Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
32. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
32Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
33. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
33Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
34. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
34Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
35. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
35Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
36. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
36Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
37. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
37Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
38. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
38Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
39. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
39Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
40. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
40Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
41. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
41Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
42. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 1RB211-24G HP compressor: stage 1
42Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
43. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 2RB211-24G HP compressor: stage 2
43Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
44. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 2RB211-24G HP compressor: stage 2
44Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
45. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 3RB211-24G HP compressor: stage 3
45Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
46. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 3RB211-24G HP compressor: stage 3
46Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
47. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 4RB211-24G HP compressor: stage 4
47Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
48. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 4RB211-24G HP compressor: stage 4
48Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
49. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 5RB211-24G HP compressor: stage 5
49Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
50. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 5RB211-24G HP compressor: stage 5
50Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
51. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 6RB211-24G HP compressor: stage 6
51Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
52. TURBO GROUP – Axial compressor theory - Variation of rotor and stator angles from root to tip
RB211-24G HP compressor: stage 6RB211-24G HP compressor: stage 6
52Axial compressor theory - Variation of rotor and stator angles from root to tip - Cheah CangTo
End of document
