1 Turbomachinery Class 11

2 Axial Flow Compressors: Efficiency Loss: Centrifugal Compressors Efficiency Loss: Axial Flow turbines: Efficiency Loss:

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

Optimization Approach A Strategy: –Find feasible solution(s) within each discipline –Use each as starting points for multi-disciplined optimization Single vs. Multi-Disciplinary Optimization –A discipline’s potential vs. a balanced design –Trading away potential in one discipline to improve another (often to find feasible design space) Pointers –Design variable count: less is more –Initially utilize large scale perturbations to identify gradients –Variable side constraints: consult with other disciplines for input

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

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7 Increasing  Note: The sign of E should be negative

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 Increasing  Note: The sign of E should be negative

Typical Optimization Formulations AeroStructures EfficiencyWeight, Pull Design VariablesObjective Function(s)Thickness distribution Chord distribution CG offsets (stacking) Design ConstraintsDesign point flow & pressure profile Off-design lapse Stability Casing clearance Material properties Stress Tuning Flutter

Airfoil Structural Overview Tools Hand calculations, finite element analysis Design responses: stress, deflection, frequencies, mode shapes Design constraints Strength, life Tuning Aero-elastic stability (flutter) HCF [High Cycle Fatigue] margin

Low Cycle Fatigue [LCF] Considerations Life Limited Parts Vs Limited Useful Life –Disks & high pressure cases – removed at end of certified life –Blades – removed for cause / wear out modes, such as airfoil erosion Assessment –Attachment fillet Kt’s available via Peterson’s or FEA –Nominal stress –S-N curve

Blade Vibration Cantilevered structures attain various modes: bending, torsion, coupled bending / torsion Each mode has its own natural frequency Effect of rotation [shaft] is to stiffen structure and raise natural frequency Structural design should be resonance free operating condition at: design speed, idle speed and other key operating points Campbell diagram shows possible matches [Excitation] between vibrational mode frequencies and multiples of shaft rotation [N] Multiples of N caused by stators, blades, struts in neighboring rows Examples: –Forced spring – mass damping –Chinook helicopter 13

Motion of a damped spring-mass system 14

Forced motion: Damped spring-mass system 15

CHINOOK HELICOPTER 16

Airfoil Tuning Represented on Campbell Diagram Airfoil frequency vs. rpm Excitation orders –Static flow disturbance relative to the rotating frame –Source = inlet distortions –Freq = EO*RPM/60 Project Requirements –1 st RL > 20% –2 nd & 3 rd RL > 5%

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HCF Strength Assessed with Goodman Diagram Steady Stress (ksi) Vibratory Stress (ksi, 0-peak) UltimateStrength AlternatingStrength AMS4928 R=-1 Goodman Diagram Smooth, Minimum Properties Vibratory Limit Steady Limit

Stresses 21

22 Secondary Air Systems

23 S SR R

24 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)

25 Turbomachinery Design Structural Considerations Blade pitch [s] at R mean 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

26 Structural Design Considerations Airfoil Centrifugal Stress Blade of constant cross section has mass:

27 Turbomachinery Design Structural Considerations Centrifugal stress is limited by blade material properties A an

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29 Turbomachinery Design Structural Considerations Centrifugal stress is limited by blade material properties Gas bending Cent. bending L From Rear

Mechanical Design – Minimizing Root Moments Blade is balanced about rim to minimize Bearing stress maldistribution Bending stress on disk web Disk rim rolling Blade airfoil is tilted to offset root bending stresses Axial & tangential tilts CG Air pressure Pull CG Offset

Turbomachinery Design Structural Considerations Bending stress on a cantilevered bead under aerodynamic loading [Kerrebrock] Centrifugal stress is typically larger than bending stress 31 c/s= 

32 Typical Centrifugal Stress Values

33 Typical Centrifugal Stress Values

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

35 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 Turbo Design - Structural Considerations

36 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:

37 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

38 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 D mean occurs on longer blades and lower flow coefficient ( )

39 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)

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

41 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 –D mean or weight and cost on  –A an or C x or weight on  –Stress level on  All turbine designs have the following conditions

42 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  A an N 2 and cost  blade count (n b )

43 Turbomachinery Gaspath Design Problem Base Case: Assume only for this case M 1 =0.8 is given.

44 Turbomachinery Gaspath Design Problem Base Case: Assume only for this case M 1 =0.8 is given.

45 Turbomachinery Gaspath Design Problem Base Case:

46 Turbomachinery Gaspath Design Problem Base Case:

47 Turbomachinery Gaspath Design Problem Baseline Design: Account for tip clearance losses as a 2% debit in efficiency Remember  cent  A an N 2 and cost  blade count (n b )

48 Turbomachinery Gaspath Design Problem Alternate Design 1: Given N, A an1 N 2, D mean1

49 Turbomachinery Gaspath Design Problem Alternate Design 1:

50 Turbomachinery Gaspath Design Problem Alternate Design 1:

51 Turbomachinery Gaspath Design Problem Summary