1. Axial Flow Compressors: 
Efficiency Loss:  
Centrifugal Compressors 
Efficiency Loss:
Axial Flow turbines: 

2. Turbomachinery Class 11

3. Configuration Selection & Multidisciplinary Decisions
Turbomachinery Design Requires Balance Between:
Performance
Weight
Cost

4. Turbomachinery Design
Several Aspects to "Cost" as seen by customer
First Cost - Price
Operating Cost - Fuel & Maintenance
Efficiency
Weight
No. of Parts
Complexity
Manufacturing
Materials
Life; Stress & Temperature

5. Turbomachinery Design
Consider Turbine Efficiency & Stress
Performance - Smith Correlation for simplicity
"A Simple Correlation of Turbine Efficiency" S. F. Smith, Journal of Royal Aeronautical Society, Vol 69, July 1965
Correlation of Rolls Royce data for 70 Turbines
Shows shape of velocity diagram is important for turbine efficiency
Correlation conditions
- Cx approximately constant
- Mach number - low enough
- Reaction - high enough
- Zero swirl at nozzle inlet
- "Good" airfoil shapes
- Corrected to zero clearance

6. Note: The sign of E should be negative
Increasing 
Note: The sign of E should be negative

7. Dixon
This is E

8. Turbomachinery Design
Efficiency Variation on Smith Curve
Increasing E from 1.33 to 2.4 [more negative] (at Cx/U=0.6):
Higher turning increasing profile loss faster than work.
Raising Cx/U from 0.76 to 1.13 (at E=1.2):
Higher velocity causes higher profile loss with no additional work
Remember - Mach number will also matter!

9. Secondary Air Systems Hot air at the top
rotating shaft is at the bottom, not visible here

10. Turbomachinery Design Structural Considerations
Centrifugal stresses in rotating components
Rotor airfoil stresses
Centrifugal due to blade rotation [cent]
Rim web thickness
Rotating airfoil inserted into solid annulus (disk rim).
Airfoil hub tensile stress smeared out over rim
Disk stress [disk]
Torsional: Tangential disk stress required to transfer shaft horsepower to the airfoils
Thermal: Stresses arising from radial thermal gradients
Cyclic effect called low-cycle fatigue (LCF)

11. Turbomachinery Design Structural Considerations
Airfoil Centrifugal Stress
Blade of constant cross section has mass:

12. Turbomachinery Design Structural Considerations
Centrifugal stress is limited by blade material properties
Aan

13. Turbomachinery Design Structural Considerations
For centrifugal stress of 40,000 lbf/in2,
AanN2 = 790,000 x 40,000=3.16 x 1010
Design practice for AN2 is from ( ) x 1010
Since N is fixed, this places upper limit on annulus area
In another, more basic form:
Where: Ut Blade Tip Speed,ft/sec
m Metal Density, lbm/in3
cent Centrifugal Stress, lbf/in2
l hub/tip radius ratio
From chart 11 

14. Typical Centrifugal Stress Values

15. Typical Centrifugal Stress Values

16. Typical Centrifugal Stress Values
Need to determine if blade with this stress level will last 1000hr to rupture

17. Turbomachinery Design Structural Considerations
Centrifugal stresses due to torsional disk stresses
The force from the change in angular momentum of gas in the tangential direction which produces useful torque.
Mw = bending moment about axial direction
Ma=gas bending moment about tangential direction [If Cx constant, pressure force produced in axial direction]
Mw is largest bending moment
Approximate form for bending stress
Design blade with centroids of cross section slightly off-center
gas bending moment is of opposite sign to centrifugal bending moment

18. Turbomachinery Design Structural Considerations
Disk & Blade Stress considerations influence selection of work and flow coefficients – from above
Selection of work and flow coefficients greatly effects blade cross sections
Following chart from former Pratt&Whitney turbine designers illustrate blade shape variation
Their meanline doesn’t exactly match Smith data

19. Turbomachinery Design Structural Considerations
Allowable stress levels are set by material properties, material temperature, time of operation and cycles of strain
Stress level measures
Ultimate stress: part fails if this level is reached
1000 hrs rupture life: part fails after 1000 hrs at a given temperature
1000 hrs creep life: part will stretch a certain percentage ( %) at a given temperature

21. S R S R

23. Turbomachinery Design Structural Considerations
Blade pitch [s] at Rmean chosen for performance s/b, h/b values
Need to check if [s] too small for disc rim attachment
number of blades have an upper limit
Fir tree holds blade from radial movement, cover plates for axial
slight movement allowed to damp unwanted vibrations
manufacturing tolerances critical in fir tree region

24. Turbomachinery Design Structural Considerations
External load due to:
airfoil, attachment & platform pull
disk lug
side plates, seals, etc.
Inertial loads due to:
centrifugal force from bore to live rim

25. Turbo Design - Structural Considerations
Airfoils inserted into slots of otherwise solid annulus [rim]
Airfoil tensile stress is treated as ‘smeared out’ over rim
Disk supports rim and connects to shaft

26. Turbo Design - Structural Considerations
Tangential disk stresses: forces on itself due to rotation
+ external (blade pull ) forces
Average Tangential Stress
Consider radial inertia load on disk element:
Noting that , an element of area in the disk cross section: X dr

27. Turbomachinery Design Structural Considerations
is the polar moment of inertia of
disk cross section about the center
line.
The total radial force becomes:
Design disk for constant stress… as r decreases, increase thickness x
Force normal to any given diameter is needed for average tangential force:

28. Turbomachinery Design Structural Considerations
note that FR Fv q
Fv/2

29. Turbomachinery Design Structural Considerations
The average tangential stress due to inertia then is:
The contribution of the external force to the average tangential stress is
so that the total average tangential stress becomes:

30. Turbomachinery Design Structural Considerations
For the same speed and pull, the average tangential stress can be reduced by:
increasing disk cross sectional area
decreasing disk polar moment of inertia - moving mass to ID of disk

31. Turbomachinery Design Structural Considerations
Rim Stress - Consider a thin ring.
Neglecting the external force, the rim inertial tangential
force is: dr X r

32. Turbomachinery Design Structural Considerations
Important Thoughts About Tangential Stress in a Ring
Wheel Speed Drives Stress, not RPM !
Hoop Stress Low at Low Wheel Speed
Ring Cannot Support Itself at High Speeds (needs a bore!)
Hoop Stress Equation Has form of Dynamic Head, a Pressure Term

34. Turbomachinery Design Structural Considerations
Average Tangential Stress in HPT disks is Increasing

35. Turbomachinery Design Structural Considerations
Conclusions:
Disk Stress Driven by Wheel Speed & Radius Ratio.
Mass at Bore Strengthens Disks
Mass at Rim Difficult to Carry
At Some Thickness, Bore is Impractical
Direct Relation Between Flow & Work Coefficients & Disk Stress

36. Turbomachinery Design Structural Considerations
Stress and major flow design parameters (, E) relate directly to achievable 
Recalling from Dimensional Analysis:
Higher stress () at constant N and Dmean occurs on longer blades and lower flow coefficient ()

37. Turbomachinery Design Structural Considerations
Also :
Flow, Density & Work are set by cycle requirements
Stress (P/A) capability is set by material, temperature, & blade configuration
Parametric effects
increased N  increased  (to first order), decreased E (to 2nd order)
increased D  decreased  (to first order), decreased E (to 2nd order)

38. Plot shows effect of +20% change in N, D & stress on Cx/U, E, and Efficiency.
Stress changes allowable blade height or annulus area.

39. Turbomachinery Gaspath Design Problem
Objective: to illustrate interaction of several design parameters
, stress level (cent), x, cost, weight flowpath dimensions
Design a baseline turbine and 3 alternative configurations
Dmean or weight and cost on 
Aan or Cx or weight on 
Stress level on 
All turbine designs have the following conditions

40. Turbomachinery Gaspath Design Problem
Design: fill in the missing blanks in the table below
Account for tip clearance losses as a 2% debit in efficiency
Remember cent  AanN2 and cost  blade count (nb)

41. Turbomachinery Gaspath Design Problem
Base Case: Assume only for this case M1=0.8 is given.

42. Turbomachinery Gaspath Design Problem
Base Case: Assume only for this case M1=0.8 is given.

43. Turbomachinery Gaspath Design Problem
Base Case:

44. Turbomachinery Gaspath Design Problem
Base Case:

45. Turbomachinery Gaspath Design Problem
Baseline Design:
Account for tip clearance losses as a 2% debit in efficiency
Remember cent  AanN2 and cost  blade count (nb)

46. Turbomachinery Gaspath Design Problem
Alternate Design 1: Given N, Aan1N2, Dmean1

47. Turbomachinery Gaspath Design Problem
Alternate Design 1:

48. Turbomachinery Gaspath Design Problem
Alternate Design 1:

49. Turbomachinery Gaspath Design Problem
Summary