1. Turbomachinery Class 12

2. Axial vs. Radial Machines
Need to determine what type of turbine is most efficient for application
- function of Ns for both compressors and turbine

3. Need to determine what type of turbine is most efficient for application
- function of Ns for both compressors and turbine

4. Radial Outflow Turbine
Ljungstrom Steam Turbine: Dixon
- steam turbine design
- No stator blades  counter-rotating blades
- radial outflow
- large amount of work per stage
- rugged

5. Radial Outflow Turbines
Ljungstrom Turbine arrangement
Compatible with expanding steam, more area with same blade height as density drops
Vaneless - Counter rotating
Old Configuration recently re-invented for gas turbines
axial counter-rotating

6. Counter-Rotating Turbines
Counter Rotation  High Stage Work
Compare:
Conventional Axial Stage, 50% Reaction & 90 Gas Turning
vs.
Counter Rotating, Vaneless Stages with 90 Gas Turning
Cx1 = Cx2, U1 = U2
 = Cx/U= 0.6
Repeating Stages
Counter Rotation  U changes direction

7. Radial Flow Turbine Analysis
Remember from Class: 1 1 2 2 3

8. Radial Flow Turbine Analysis
In this problem, for the axial stage
- n=0.6, R=0.5, and b1-b2=a1-a2=90
- Iteration:
Guess b1
From Calculate E.
From Calculate b2
Iterate until turning (b1-b2=90) is correct
For the counter-rotating stage…..match turning

9. Radial Flow Turbine Analysis Conventional vs Counter-Rotating
Counter-rotating: high stage work (E)

10. Radial Flow Turbine Analysis - Conventional Design

11. Radial Flow Turbine Analysis - Counter-Rotating Design

12. Radial Inflow [900 IFR] Turbines
Kinematic view
Thermodynamic view
Exit part of rotor (exducer) is curved to remove most of tangential component of velocity
Advantage of IFR turbine: efficiency equal to axial turbine, greater
amount of work per stage, ease of manufacture, ruggedness

13. Radial Flow Turbines
Radial Inflow Turbine with Scroll

14. Radial Flow Turbines
Radial Inflow Turbine Stator/Rotor

15. Radial Flow Turbines
Radial Inflow Turbine Stator/Rotor [No shroud]

16. Radial Flow Turbines Radial Inflow Turbine Scroll
Scroll or distributor
- streamwise decreasing cross flow area
- provide nearly uniform properties at exit

17. Radial Flow Turbines
Radial Inflow Turbine Scroll - Stator

18. Radial Flow Turbines Radial Inflow Turbine Impeller Note
- direction of rotation
- rotor rearward curvature

19. Radial Flow Turbine Design
Nominal Stator / Rotor Design:
Station 1 – Inlet to Stator
Station 2 – Exit of Stator, Inlet to Rotor
[Radially inward]
Station 3 – Exit of Rotor
[Absolute velocity is axial]
Station 4 - Exit of Diffuser
Rotor inlet relative velocity is radially inward
- For Zero Incidence at Rotor Inlet, W2=Cr2 and Cq2=U2
Rotor exit absolute flow is axial
- For Axial Flow at Rotor Exit, C3=Cx3 and Cq3=0 C2
Cm2=Cr2=W2 U2
Cm3=C3=Cx3 U3 W3  

20. Radial Flow Turbine Design- 900 IFR
For adiabatic irreversible [friction] processes in rotating components
From the Alternate Euler Equation:
and

21. Radial Flow Turbine Design
substituting:
Thus from Alternate Euler’s Equation :

22. Radial Flow Turbine Design
Example: Dixon 8.1
The rotor of an IFR turbine, designed to operate at nominal condition,
Diameter is cm and rotates at 38,140 rev/min.
At the design point the absolute flow angle at the rotor entry is 72 deg.
The rotor mean exit diameter is ½ the rotor diameter
The relative velocity at the rotor exit is twice the relative velocity at the inlet.

23. Radial Flow Turbine Design
Example: Dixon 8.1

24. Radial Flow Turbine Design
Example: Dixon 8.1

25. Radial Flow Turbine Design
Example: Baskharone p
0=inlet =stator exit =rotor inlet 3=rotor exit
Stator / nozzle exit Mach number M1=0.999

26. Radial Flow Turbine Design
Example: Baskharone p cont’d
In constant area interstage duct, apply free-vortex condition to flow from stator exit to rotor inlet

27. Radial Flow Turbine Design
Mollier Diagram for Radial Flow Turbine (Dixon): s
1/2 C2spouting

28. Radial Flow Turbine Design
Spouting Velocity [from hydraulic turbine practice]:
Spouting Velocity, C0: the velocity which has an associated kinetic energy equal to the isentropic enthalpy drop from the turbine inlet stagnation pressure P01 to the final exhaust pressure.
By taking the exhaust pressure as the isentropic exit static pressure, and assuming no diffuser, then
For an ideal radial turbine with KE recovery, this leads to or

29. Radial Flow Turbine Design
Nominal Design Point Efficiency:
Efficiency is centrifugal devices is often represented by total-to-static conditions: ts = total-static

30. Radial Flow Turbine Design
The enthalpy losses for the stator (nozzle) and rotor can be expressed as a fraction, z, of the exit kinetic energy:
For a constant pressure process, ds = dh/T so that:

31. Radial Flow Turbine Design
Substituting into the efficiency definition:
For the Nominal Design Point velocity triangles, we see that:

32. Radial Flow Turbine Design
Substituting, we get for the efficiency:
The temperature ratio, T3/T2, generally only has a very minor effect on the value of hts so that it can be neglected.

33. Radial Flow Turbine Design
In addition, the values of r3 and b3are taken to apply at the mean exit radius of the rotor, i.e. r3 = ½ (r3h+ r3t), so that:
Read Dixon Example 8.2, page 254

34. From Centrifugal Compressor Notes
Slip: flow does not leave impeller at metal angle [even for inviscid flow]
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

35. Radial Flow Turbine Design
Static pressure gradient across passage causes streamline to shift flow towards suction surface
In reality, the incidence to the rotor varies over the pitch of the rotor as:
due to
Potential and wake interaction with the vane.
Relative eddy effect seen at exit of compressor
Effect produces a LE slip factor
This variation over the pitch leads to an
- optimal incidence and
- optimal number of blades
where the efficiency of the rotor is a maximum.
P=pressure
S=suction

36. Radial Flow Turbine Design
Rotor Inlet Velocity Triangle (with incidence):
Average relative velocity W and avg. relative incidence 2
If we define an incidence factor, l [like  slip factor in compressors]: C2 W2
CR2=CM2
CU2 U2

37. Radial Flow Turbine Design
From the work of Stanitz regarding slip factors:
Then from the rotor inlet velocity triangles, the inlet flow angle to the rotor is:

38. Radial Flow Turbine Design
Criteria for the Optimal Number of Blades:
Jamieson model

39. Radial Flow Turbine Design
Criteria for the Optimal Number of Blades:
Optimum blade number balances loading & friction
Rohlick model uses (quantities at the inlet to rotor):
Jamieson model

40. Radial Flow Turbine Design
Other Correlations for Optimal Number of Blades (Rohlick results similar to Jamieson):
from Dixon

41. This is to clarify some of the confusing notation in Dixon regarding blade count
Stanitz correlation
uses blade number and flow coefficient to calculate the relative radial turbine exit flow angle.
Other correlations
uses semi-empirical expressions for calculating the optimum [minimum] blade count Z for an optimum efficiency design, where
For such a design the exit flow will be radial [in the absolute frame], therefore 2=0 and the correlations are in terms of the corresponding absolute frame air angles [2], e.g.

42. This is to clarify some of the confusing notation in Dixon regarding blade count
Jamieson
Rohlik

43. Radial Flow Turbine Design
Specific Speed relates impeller shape & velocity diagram
Rohlick shows:
where

44. Efficiency [ts] of 900 IFR Turbine with Ns [Rohlick analysis]

45. Efficiency [ts] of 900 IFR Turbine with Ns [Rohlick analysis]
Dixon Fig. 8.14
Ns units: Nondimensional=radians

46. Radial Flow Turbine Design
Rohlik Model shows Distribution of Losses
Clearance: pressure
diff. effects between
rotor and shroud
Windage: friction effects
between rotor and
shroud

47. Radial Flow Turbine Design
Flow Path Shape is Related to Specific Speed
Maximum efficiency designs