1. Turbomachinery Centrifugal Compressors Class 13

2. Centrifugal Compressor Design
Geometry
Rothalpy
Impeller Design Considerations
Eye – Inducer
Slip
Diffuser Design Considerations
Volute Design Considerations

3. Centrifugal Compressor Components

4. Centrifugal Compressor Components
Collector scroll and vanes may be replaced with vaneless diffuser

5. Centrifugal Compressor Components
Centrifugal compressor= impeller+diffuser
Geometrical Definitions
Eye: L.E. of impeller
Impeller: raises energy level of fluid by
increasing radius
Inducer: portion of impeller from eye to
region where flow turns radial
Diffuser: converts K.E. from impeller into
P.E.. Adding vanes reduces
size of diffuser
Scroll or volute: collects flow from diffuser
and delivers to outlet

6. Centrifugal Compressor Design
Compressor’s role is to produce high pressure flow
High pressure is achieved by imparting kinetic energy to flow by impeller / rotor.
Kinetic energy is converted to high pressure in diffuser / stator.
As radius increases, pressure increases
½ pressure rise in impeller passage
½ pressure rise in diffuser passage
Diffuser may have vanes, but stator passages must have increasing area
Volute cross-section area increases gradually to exit

7. Centrifugal Compressor Design
In class we defined "Rothalpy" for rotors:
Since across the impeller I1=I2 then the change in swirl velocity U
explains why static enthalpy rise is so large for centrifugal compared to single-stage axial compressors
If no prewhirl Cu1=0
See result shown later is Example 1

9. Centrifugal Compressor Design: T.E.
Blade TE shape for opt. performance
Forward: against rotation
Radial
Backward: with rotation

10. Straight
Back
Forward

11. Centrifugal Compressor Design: T.E.
Radial T.E.
Ideal no-slip view
Increased Cr/Wr for same U does not change Cu or work
T02/T01 unchanged with increased Cr

12. Centrifugal Compressor Design: T.E.
Backward T.E.
Increased Cr/Wr for same U decreases Cu or work
T02/T01 decreases with increased Cr
Stable side of compressor map

13. Centrifugal Compressor Design: T.E.
Forward T.E.
Increased Cr/Wr for same U increases Cu or work
T02/T01 increases with increased Cr
Unstable side of compressor map

14. Centrifugal Compressor Design: T.E.
Radial T.E.

15. Centrifugal Compressor Design: T.E.
Radial: dotted triangle
Backswept: solid
Same radial component,
same mass flow
Relative velocity increased,
absolute decreased
Increases efficiency, but
reduces work absorbing
capacity [Cw2 lower]
Backswept Impellor

16. Centrifugal Compressor Design: T.E.

17. Centrifugal Compressor Design: L.E.
Prewhirl [in the direction of rotation] added from added upstream guide vanes
In high PR compressors, may be necessary to provide prerotation to reduce high relative inlet velocity. Also reduces incidence / reduces twist  lower bending stresses
Vane radial design impact on inducer
Free vortex Cu  1/r: high incidence at low rh/rt designs
Forced vortex Cu  rn Wo Wn
- IGV will allow untwisted impellor inlet
- Untwist will reduce rotor root bending
stresses

18. Centrifugal Compressor Design: Tip
Tip Leakage Issues
Flow from pressure [+] to suction [-] side over tip
Flow from downstream [+] to upstream [-]

19. Review: Axial Compressor Slip
Slip: flow does not leave impeller at metal angle
Carter's Rule:
Blade turning & solidity are important
Viscosity plays small role within low loss incidence range
T.E. thickness & shape significant

20. Centrifugal Compressor Slip
Slip: flow does not leave impeller at metal angle [even for inviscid flow] – due to less than perfect guidance from blade.
If absolute flow enters impeller with no swirl, =0.
If impeller has swirl (wheel speed) , relative to the impeller the flow has an angular velocity -  called the relative eddy [from Helmholtz theorem].
Effect of superimposing relative eddy and through flow at exit is one basis for concept of slip.
Relative eddy
Relative eddy with throughflow

21. Centrifugal
Compressor
Slip

22. Axial Compressor Slip

23. Axial Compressor Slip

24. Centrifugal Compressor Slip
"Slip" (Deviation) Reduces Swirl & Work
Slip Factor Vs

25. Centrifugal Compressor Slip
Several Correlations for Centrifugal Impeller Slip Factor
Weisner
Stodola
Stanitz

26. Centrifugal Compressor Design
In general, with possible prewhirl Cu10
Introduce work done-input factor 
In turbines [work done]  < 1, due to boundary layer effects
In compressors [work input]  > 1, need more power to account for boundary layer effects

27. Centrifugal Compressor Design
Impeller Performance Effects:

28. Centrifugal Compressor Design
Backward sweep
Splitter impeller vane
Reduce effect of slip by using splitter vane to reduce diffusion

29. Centrifugal Compressor Design
Calculate inlet blade angle at root and tip
Calculate Mach number at eye tip
Assume no whirl at inlet
Axial velocity can be determined from continuity but
density needs trail and error iteration

30. Centrifugal Compressor Design
Assume no more iteration is needed

31. Centrifugal Compressor Design

32. Centrifugal Compressor Design
Example #2: Dixon 7.1
A radial vaned centrifugal impeller is required to provide a supply of pressurized air to a furnace. The specification requires that the fan produce a p0 rise equal to 7.5 cm of water at a volumetric flow rate (Q) of 0.2 m3/s.
The fan impeller is made from [Z=30] thin sheet metal vanes, the ratio of the passage width to exit height=2 and r=0.1.
Assume ad=0.75, m=0.95, slip can be estimated from Stanitz correlation
Assume R=287 J/(kg-C), p01=101.3 bar, T01=288K
Assume

33. Centrifugal Compressor Design
1- Determine the impeller vane exit speed
2- Determine the volumetric flow rate
Stannitz
21.98

34. Centrifugal Compressor Design
2- Determine the volumetric flow rate cont’d
3- Power required if mechanical efficiency is 0.95
4- Determine specific speed
No swirl

35. Axial vs. Radial Machines

36. Diffuser Design: Sta. 23 Rotation Effect on Diffuser Pressure Rise
Rotation reduces boundary layer thickness and limits pressure rise in radial portion of impeller
Johnston & Rothe varied area ratio & rotational speed in 2D diffuser test
Rotated Diffuser with flow axis radial

37. Centrifugal Compressor Design
Example #3: Will work through design of each component separately
Know U2, slip, not p02, T02, 

38. Centrifugal Compressor Design: Sta. 1

39. Centrifugal Compressor Design: Sta. 2

40. Centrifugal Compressor Design: Sta. 2

41. Centrifugal Compressor Design
Impeller Performance:
Efficiency up to 90 to 95% Polytropic
Small size reduces efficiency
Thickness, finish affect performance
Clearance
Multi-stage usually shrouded because axial location (and therefore, ) difficult to control

42. Diffuser Design: Sta. 23 Basic Parameters h = height of 2D diffuser
Y = entrance width
L = Length
B = entrance boundary layer blockage
W = inlet velocity
Rotation Number h

43. Diffuser Design: Sta. 23

44. Radial Diffuser Performance: Sta. 23
Pressure coefficient [compressor-type definition]
Effectiveness, Diffuser Efficiency

46. Diffuser Issues
Jet Flow
Appreciable Stall
No Stall

47. Radial Diffuser Design: Sta. 23
Diffusers for Centrifugal Impellers:
Rotor Exit Flow Often Contains:
High Swirl up to 80
High Velocity M>1 often
Distortion Impeller Separation
Unsteady Flow Rotating Distortion

48. Radial Diffuser Design: Sta. 23
Diffuser reduces velocity & swirl
Diffuser Configurations:
Vaneless inexpensive, limited effectiveness,
work over wide range of operation, large, ok for industrial use
Vaned more expensive, better performance, smaller, sensitive to incidence effects
Pipe most expensive, best performance, compact, complete angle control

49. Vaneless Diffuser Performance: Sta. 23
Vaneless Diffuser: removes swirl of fluid by increasing radius
Continuity:
Inviscid Tangential Momentum, (Friction Important for quantitative calculations!).
For constant angular momentum:

50. Vaneless Diffuser Performance: Sta. 23
Swirl angle
Increases - compressible flow
Constant - incompressible flow
Reduced by friction

51. Vaneless Diffuser Performance: Sta. 23
Flow trace for vaneless, incompressible diffuser
Ex: Radius ratio=2, =77.6: =180 ! In other words, radius will grow by factor of 2.26 as flow revolves 1800 around the diffuser
Lot's of friction in Vaneless Diffusers
Flow path in vaneless, incompressible diffuser is log spiral outward radially and circumferentially

52. Vaneless Diffuser Performance: Sta. 23
Diffuser Flow not Simple
1D Inviscid Analysis with Momentum and Continuity Gives Incorrect Pressure Rise in Diffuser (Too High)
Need More Physics for Valid Solution – Friction !

53. Centrifugal Compressor Design: Sta. 23

54. Vaned Diffuser Design: Sta. 23
Vaned Diffusers
Vanes added to remove swirl of fluid at a higher rate than done by increasing radius
Better Performance BUT matching is critical
Steifel 1972
34% increase in throat area, same vane shape
15% greater rotor flow

55. Vaned Diffuser Design: Sta. 23
Diffuser Performance
Rundstadler & Deane 2D & Conical diffusers
Large Range of:
Area Ratio
Length/Height
Aspect Ratio
Mach No.
Reynolds No.
Blockage
Effect of increasing diffuser angle: range of steady and transient flows
Blockage drives effectiveness!

56. Vaned Diffuser Design: Sta. 23
Diffuser Geometry
Throat area is critical
Pipe Diffuser better with M>1

57. Vaned Diffuser Design: Sta. 23
Throat Blockage Drives Effectiveness

58. Vaned Diffuser Design: Sta. 23
Throat Blockage Driven by diffusion between blade exit and throat

59. Volute and Vaneless Diffuser: Sta. 34
Impeller, Vaneless Diffuser, and Volute

60. Volute: Sta. 34 Radius characteristic of volute is Rv
Rv is function of angular position,
usually linear from entrance to exit

61. Volute Design Volute Design Considerations
Effects overall performance
Tongue aligned at only one Cx/U
Pressure Loss
Space requirements
Flow Uniformity

62. Volute Design
Volute designed for uniform flow around circumference at diffuser exit
Angular momentum sets swirl velocity
Volute area set to match uniform flow from diffuser by angular momentum and continuity

63. Volute Design
Common design practice is to maintain simple conservation of angular momentum along mean streamline in volute [r=rV]

64. Volute Design The Best Volute Design is Not Perfect
Stagnation point on tongue creates local high pressure
Curvature stops at end of volute changing radial
pressure gradient
Tongue incidence at off-design 3 creates general distortion
Vanes or dual volutes used to reduce distortion

65. Volute Design .

66. Volute Design
Volute exit radial velocity is arbitrary and can be changed to optimize diffusion.

67. Volute Design

68. Volute Design

69. Volute Design

70. Volute Design