1. Centrifugal Compressors
Classes and comparisons between compressors
Axial
Centrifugal
Function
Large engine
Small engine
Engine type
Very large (> 100 kg/s)
< 15 kg/s
Mass flow rate
High 94 %
Low %
Efficiency
large
small
# of stages
Low (<1.5)
High (5-7)
Pressure ratio per stage
Low, thus allow using many stages
High for more than one stage
Pressure loss
Not easy
easy
Fixing and manufacturing
Very expensive
Cheap, wider operating range
Cost

2. Centrifugal Compressors
Principle of Operation
Centrifugal compressors consist of stationary casing containing
Rotating impeller (imparts a high velocity of air),
Fixed diverging passage (The air is decelerated with rise in static pressure).
Impeller may be single or double-sided

3. Centrifugal Compressors
Air is sucked into the impeller eye and whirled at high speed by the vanes of the impeller disc.
The static pressure increases from eye to tip.
Remainder of static pressure rise occurs in diffusers.
Normally half of pressure rise occurs in the impeller and 50% in diffuser.
Some stagnation pressure loss occurs.

4. Centrifugal Compressors

5. Centrifugal Compressors
Work done and Pressure Rise:
Absolute velocity of air at impeller tip.
tangential or whirl component
radial component.
 is the angle given by the direction of the relative velocity at inlet V1. Also this is the angle of leading edge of the vane with tangential direction.
Slip phenomenon: air trapped between the impeller vanes does not move with the impeller, thus air acquire whirl (Cw) velocity at the tip which is less than u. :

6. Centrifugal Compressors

7. Centrifugal Compressors
Velocity diagrams

8. Centrifugal Compressors
Considering unit mass of air:
momentum equation

9. Centrifugal Compressors=
With state 1 as inlet to rotor
“ as exit from rotor
“ as exit of diffuser
No energy addition in diffuser
Thus

10. Centrifugal Compressors
Defining c as overall isentropic efficiency, then overall stagnation pressure ratio is given by :

11. Centrifugal Compressors
Example 4.1
The following data are suggested as a basis for the design of a single-sided centrifugal compressor:
Power input factor = =1.04
Slip factor  = 0.9
Rotational speed, N= 290 rev/s
Overall diameter of impeller, D=0.5m
Eye tip diameter=2re=De=0.3m
Eye root diameter, D1=2r1=0.15m
Air mass flow, m=9 kg/s
Inlet stagnation temperature To1= 295
Inlet stagnation pressure Po1 = 1.1 bar
Isentropic efficiency, c=0.78

12. Centrifugal Compressors
Requirements are
(a) to determine the pressure ratio of the compressor and the power required to drive it assuming that the velocity of the air at inlet is axial.
(b) to calculate the inlet angle of the impeller vanes at the root and tip of the radii of the eyes, assuming that the axial inlet velocity is constant across the eye annulus; and
(c) to estimate the axial depth of the impeller channels at the periphery of the impeller.

13. Centrifugal Compressors
(a) impeller tip speed
Temperature equivalent of the work done on unit mass flow of air, is

14. Centrifugal Compressors
Power required=
(b) to find the inlet angle it is necessary to determine the inlet velocity which in this case is axial; .
Since the density 1 depends upon C1and both are unknown, a trial and error process is required.

15. Centrifugal Compressors
Flow triangles
u2=455.5 m/s
Assume axial flow
two unknown (,c) in one equation but another relation is given by

16. Centrifugal Compressors
Note this is normal to design for an axial velocity of about 150 m/s, this providing a suitable compromise between high flow per unit frontal area and frictional losses in the intake.
Annulus area of impeller eye,
Based on stagnation conditions:

17. Centrifugal Compressors
, the equivalent dynamic temperature is

18. Centrifugal Compressors
equivalent dynamics temperature is

19. Centrifugal Compressors

20. Centrifugal Compressors
This is a good agreement and a further trial using Ca1=143 m/s is unnecessary because a small change in C has little effect upon .
For this reason, it is more accurate to use the final value 143 m/s, rather than the mean of 145 m/s ( the trial value) and 143 m/s.
The vane angles can now be calculated as follows:
and at eye root radius =136.5 m/s,

21. Centrifugal Compressors
 at root=tan-1(143/136.5)=46.33,
 at tip =tan-1143/273=27.65
(c) the shape of the impeller channel between eye and tip is very much a matter of trial and error.
The aim is to obtain as uniform a change of flow velocity up the channel as possible, avoiding local decelerations up the trailing face of the vane.
To estimate the density at the impeller tip, the static pressure and temperature are found by calculating the absolute velocity at this and using it in conjunction with the stagnation pressure which is calculated from the assumed loss up to this point.

22. Centrifugal Compressors

23. Centrifugal Compressors
To calculate density at exit

24. Centrifugal Compressors
thus get 2.

25. Centrifugal Compressors

26. Centrifugal Compressors
The required area of cross-section of flow in the radial direction at the impeller tip is

27. Computational Design of a Centrifugal Compressor
PROGRAM MAIN
COMMON CP,R,GAMRAT
COMMON VECT(5000,500) C
C OPEN(30,FILE='D:\Dif\GRIDG.RES')
OPEN(5,FILE='C:\CALCULATIONS\Data_PyT10_6.1mps_D50mmFdn.txt')
OPEN(6,FILE='C:\CALCULATIONS\OUT.txt')
OPEN(7,FILE='C:\CALCULATIONS\output data for drawings.txt')
OPEN(8,FILE='C:\CALCULATIONS\OUT2.txt')
C OPEN(30,FILE='C:\Dif\GRIDG.RES')
C OPEN(6,FILE='C:\Dif\Conv 1\GRIDG.OUT')
C OPEN(5,FILE='C:\dif\Conv 1\GRIDG.DAT')
C OPEN(30,FILE='C:\Dif\Conv 1\GRIDG.RES',FORM='UNFORMATTED')
C OPEN(6,FILE='C:\Dif\GRIDG.OUT')
C OPEN(5,FILE='C:\dif\GRIDG.DAT')
C OPEN(6,FILE='D:\Dif\GRIDG.OUT')
C OPEN(5,FILE='D:\dif\GRIDG.DAT')

28. Computational Design of a Centrifugal Compressor
PI=22./7.
EPSI=1.05
SIGMA=0.9
RPM=305.
D0=0.6
DIT=0.4
DIR=0.15
FLOW=14
TO1=300
PO1=100.
EFFC=0.8
CP=1005
EFFIMP=0.89
GAMMA=1.4
R=0.287
GAMRAT=GAMMA/(GAMMA-1.)
U=PI*D0*RPM
TO13=EPSI*SIGMA*U*U/CP
PO13=(1.+EFFC*TO13/TO1)**GAMRAT
TO3=TO1+TO13
TO2=TO3
PO3=PO1*PO13
POWER=FLOW*CP*TO13/1000.
WRITE(6,11)POWER,TO13,U,PO13
11 FORMAT(2X,'POWER=',E13.4,/2X,'TO13=',E13.5/2X,'U=',E13.5/3X,
1'Press ratio=',E13.4//)
AI=PI*(DIT**2-DIR**2)/4.

29. Computational Design of a Centrifugal Compressor
CALL SITER(C1,TO1,PO1,AI,FLOW)
C WRITE(6,12)C1,EPS,P1,T1,AI
C 12 FORMAT(2X,E13.3/4E13.4)
UE=PI*DIT*RPM
UR=PI*DIR*RPM
ALFAR=ATAN(C1/UR)*180./PI
ALFAT=ATAN(C1/UE)*180./PI
WRITE(6,24)
24 FORMAT(8X,'ALFAT, ALFAR'/)
WRITE(6,13)ALFAT,ALFAR
13 FORMAT(2X,2E13.3)
C Axial Depth CR=C1
CW=SIGMA*U
CSQ=CR*CR+CW*CW
PO2=PO1*(1.+EFFIMP*TO13/TO1)**GAMRAT
T2=TO2-CSQ/(2.*CP)
P2=PO2*(T2/TO2)**GAMRAT
RHO2=P2/(R*T2)
A2=FLOW/(RHO2*CR)
AXDEPTH=A2/(PI*D0)
WRITE(6,17)AXDEPTH
17 FORMAT(//10X,'Axial Depth= ', 10X, E13.5)

30. Computational Design of a Centrifugal Compressor
C CALL PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)
STOP
END
SUBROUTINE SITER(C,TO,PO,A1,FLOW)
COMMON CP,R,GAMRAT
C WRITE(6,102)C,EPS,PO,TO,A1
RHO1=PO/(R*TO)
10 C=FLOW/(RHO1*A1)
T=TO-C*C/(2.*CP)
P=PO*(T/TO)**GAMRAT
23 FORMAT(7X,'C',18x,'EPS',8X,'P',8X,'T',15X,'A1'/)
C WRITE(6,102)C,EPS,P,T,A1
RHONEW=P/(R*T)
EPS=ABS((RHONEW-RHO1))/RHONEW
IF(EPS.LT.0.001)GO TO 20
RHO1=RHONEW
GO TO 10
20 CONTINUE
WRITE(6,23)
WRITE(6,102)C,EPS,P,T,A1
102 FORMAT(2X,5E13.4/)
Return
End

31. Computational Design of a Centrifugal Compressor
SUBROUTINE PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)
COMMON VECT(5000,500),WMAS(5000,500),BETA(5000,500),PI
FLOW=10.
DFLOW=FLOW/10.
WRITE(6,30)POWER,TO1,PO1,EFFC,GAMRAT,CP
30 FORMAT(6E13.3)
DO 10 I=1,9
TO3=TO1+POWER*1000./FLOW/CP
PO3=PO1*(1.+EFFC*(TO3-TO1)/TO1)**GAMRAT
FLOW=FLOW-DFLOW
C WRITE(6,20)TO3,PO3
WRITE(6,20)FLOW,PO3/PO1
20 FORMAT(2E13.3)
10 CONTINUE C
RETURN
END

32. Centrifugal Compressors
The Diffuser:
In the case of gas turbine, the air should exit the diffuser and enters the combustion chamber at minimum velocity.
Thus, design of diffuser requires that only a small part of strengthening temperature is K.E. normally u=90m/s at exit of the compressor.
rapid divergence is not recommended
optimum angle is 7.0.
Neglecting losses, thus, angular momentum r C=constant
Cr: radial velocity will also decrease.

33. Centrifugal Compressors
Example 4.2 Consider the design of a diffuser for the compressor dealt with in the previous example. The following additional data will be assumed: Radial width of vaneless space wd = cm Approximate mean radius of diffuser throat, rm =0.033m
Depth of diffuser passages dd Number of diffuser vanes nv 12 Required are (a) the inlet angle of the diffuser vanes and (b) the throat width of the diffuser passages which are assumed to be of constant depth
Consider conditions at the radius of the diffuser vane leading edges, at r2= =0.3m. Since in the vaneless space r Cw =constant for constant angular momentum,

34. Centrifugal Compressors
The radial component of velocity can be found by trial and error. The iteration may be started by assuming that the temperature equivalent of the resultant velocity is that corresponding to the whirl velocity, but only the final trial is given here.

35. Centrifugal Compressors
Ignoring any additional loss between the impeller tip and diffuser vane leading edges at 0.3m radius, the stagnation pressure will be that calculated for the impeller tip, namely it will be that given by

36. Centrifugal Compressors
Area of cross-section of flow in radial
Check on Cr2:
Cr2=Taking Cr as 97.9 m/s, the angle of the diffuser vane leading edge for zero incidence should be

37. Centrifugal Compressors
the throat width of the diffuser channels may be found by a similar calculation for the flow at the assumed throat radius of 0.33m.
Try Cr2= 83 m/s

38. Centrifugal Compressors
Area in radial direction=A (radial) = 2Db =0.0365

39. Centrifugal Compressors
Compressibility Effects
At the impeller inlet,( eye of the impeller), the relative velocity is high and could be very close to sound values.
No problem at sea level conditions, however at high altitude ( aircraft engine), speed of sound decreases and we might have supersonic flow.
For example at m, T=217 K

40. Centrifugal Compressors
we try to avoid this by having guide vanes and it is better to be variable in the case of change of conditions, such as altitude.
By trial and error, the value of Ca can be determined from Ca and , C1t 9and C1t can be determined. Then value V1t9can be determined which is smaller.=239 m/s.
For this design, the flow is subsonic at altitude.
Trying

41. Centrifugal Compressors
For 30 pre whirl
C1=150/cos30=173.2

42. Centrifugal Compressors
In spite of the advantage, it has a disadvantage of reducing the pressure ratio of compressor.

43. Centrifugal Compressors
for details see text book

44. Centrifugal Compressors
Vaneless diffusers:
For vaneless diffuser, no problem, it can handle supersonic flow while vaned diffuser can’t.
At the exit of the vaneless diffuser, C3=355, M2=0.56<1.0, which is subsonic and is ok for vaned diffuser.
Advantages of vane less diffuser:
Mach number M2 could be supersonic without
Vaneless space will eliminate any non-uniformity of the flow coming out of the impeller ( jets and wakes).
This is good to avoid any problem in exciting the vanes.
As a normal practice, no. of vanes in the diffuser is less than impeller blades.
N (vanes)<N (impeller)

45. Centrifugal Compressors
Non-dimensional quantities for compressor characteristics:
D=diameter, N=rpm, m=mass flow rate
po1=inlet pressure, po2=exit pressure
T01=inlet temperature, To2=exit temperature
N=no. of variables
M=basic dimensions
there are 7 variables, 3basic dimensions (M,L,T)
and  terms 7-3=4.

46. Centrifugal Compressors
Stall
Defined as the (aerodynamic stall) or the break-away of the flow from the suction side of the blades.
A multi-staged compressor may operate safely with one or more stages stalled and the rest of the stages unstalled . but performance is not optimum. Due to higher losses when the stall is formed.
Surge
Is a special fluctuation of mass flow rate in and out of the engine. No running under this condition.
Surge is associated with a sudden drop in delivery pressure and with violent aerodynamic pulsation which is transmitted throughout the whole machine.

47. Centrifugal Compressors

48. Centrifugal Compressors