1. Turbomachinery Design Considerations
EGR 4347 Analysis and Design of Propulsion Systems

3. Euler Pump Equation

4. Compressor Axial Schematic

5. Compressor Centrifugal Schematic

6. Compressor Typical Velocity Diagram

7. Compressor Repeating Row Nomenclature

8. Airfoil Pressure and Velocity

9. Important Parameters Compressor Efficiency, c Stage Efficiency, s
Polytropic Efficiency, ec
Stage Pressure Ratio, s
Overall Pressure Ratio, c

10. Degree of Reaction
Desirable value around 0.5

11. Diffusion Factor
Quantifies the correlation between total pressure loss and deceleration (diffusion) on the upper (suction) surface of blade (rotor and stator)
 is the solidity – the ratio of airfoil chord to spacing

12. Diffusion Factor Data

13. Hub, Mean, and Tip Velocity Diagrams

14. Stall and Surge

15. Parameters Affecting Turbine Blade Design
Vibration Environment
Number of Blades
Tip Shroud
Airfoil Shape
Inlet Temperature
Trailing-Edge Thickness
Blade Cooling
Allowable Stress Levels (AN2)
(N = Speed, RPM)
Material
Service Life Requirements

16. Turbine Prelim Design Focuses on Defining a ‘Flowpath’ that Meets Customer Requirements
Customer Req’ts/Desires
Performance
Mission
Cost & Risk
FN, SFC Req’ts
Aero Technology
Life Req’ts Mech. &
Cooling Technologies
Performance
Cycle Design
Material
Selections
Combustor
Design
Component
Temp to other
areas
Turbine
Aero Design
Turbine
Mech Design
AN2
wrh
a,b Wc
Clearance
Manufacturing No No
Yes
Meet Requirements
Preliminary Design = “Frozen” Turbine Flowpath

17. Turbine Mechanical Detailed Design
Detailed Design Accomplishes Two Functions:
Verify Assumptions/Choices Made in Preliminary Design
Provide Detailed Geometry Required to Achieve Preliminary Design Goals
Detail Mechanical Design Disciplines:
Materials Selection - satisfy life/performance goals
Secondary Flow Analysis - define/control nonflowpath air (e.g. cooling)
Heat Transfer - component temperature definition
Stress Analysis - component stresses
Vibration Analysis - design to avoid natural frequencies
Life Analysis - define component life for all failure modes

18. Turbine Nomenclature

19. 50% Reaction Turbine

20. 0% Reaction or Impulse Turbine

21. Hub, Mean and Tip Velocity Diagrams

22. Velocity Triangles “ABSOLUTE” FLOW ANGLES “RELATIVE” BLADE ANGLES
Relating a’s and b’s

23. TURBINE ANALYSIS –
Velocity Triangles

24. TURBINE ANALYSIS Euler Turbine Equation: v2 V2 u2 inlet, i v3 u3
exit, e V3
convention:
v3 = -ve
also, ri = re= r

25. TURBINE ANALYSIS Turbine Efficiency: Stage Loading Coefficient, y:
Adiabatic (Isentropic)
Polytropic
Stage Loading Coefficient, y:
Typical values:

26. TURBINE ANALYSIS Flow Coefficient, F: Typical values 0.5 - 1.1
Degree of Reaction, °R:
°Rt = 0 Impulse turbine
Reaction turbine

27. TURBINE ANALYSIS Pressure Loss Coefficient, ft:
Velocity Ratio, VR: Typical values:
Tip Leakage
Cooling Loss
Profile Loss
Endwall Loss

28. Turbine Mechanical Design
AN2: Rotor Exit Annulus Area x [Max Physical Speed]2
Units: in2 x RPM2 x 1010, typical values: 0.5<AN2<10 x1010
Typical Limits:
Cooled Blade < 5 x 1010
Advanced Technology < 6.5 x 1010
Uncooled Solid Blade < 10 x 1010
LPT < 7 x 1010
Use max physical speed; not design point or TO speed
Blade Airfoil Stress is Primarily Driven by AN2
Blade Pull Load Driven by AN2

29. Turbine Mechanical Design – Hub and Tip Speed Limits
rhw2: Hub radius x 2p/60 x Max Physical RPM
Units: ft/s
Typical Values:
HPT ft/s < rhw2 < 1500 ft/s
LPT ft/s < rhw2 < 1000 ft/s
Use max physical RPM; not design point or TO speed
Disk Stress is Driven Primarily by rhw2
Disk and Blade Attachment Stresses are a function of rhw2 and AN2

30. Structures - Rotational Stress (Centrifugal Stress)
- Bending Stress due to the lift of “airfoils”
- Buffet/Vibrational Stress
- Flutter due to resonant response
- Torsion from shaft torque
- Thermal Stress due to temperature gradients
- FOD
- Erosion, Corrosion, and Creep

31. Structures

32. Structures

34. Structures - Stress Calculations
- Rotational Stress (Centrifugal Stress)
-- Same as for compressor, sc, sblade
- Disk Thermal Stress, st
-- assume T = T(r) = T0 + DT(r/rH)
-- a - coef of linear thermal expansion
-- E - Modulus of Elasticity rH T T0
T+DT r rH
Disk r q
radial stress
tangential stress