Turbomachinery Class 11

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TurbomachineryClass 11
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• Axial Flow Compressors 
• Efficiency Loss  
• Centrifugal Compressors 
• Efficiency Loss
• Axial Flow turbines 
• Efficiency Loss

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Configuration Selection Multidisciplinary
Decisions

• Turbomachinery Design Requires Balance Between
• Performance
• Weight
• Cost

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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 disciplines 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

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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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Increasing ?
Note The sign of E should be negative
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Turbomachinery Design

• Efficiency Variation on Smith Curve
• Increasing E from 1.33 to 2.4 more negative (at
  Cx/U0.6)
• Higher turning increasing profile loss faster
  than work.
• Raising Cx/U from 0.76 to 1.13 (at E1.2)
• Higher velocity causes higher profile loss with
  no additional work
• Remember - Mach number will also matter!

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Increasing ?
Note The sign of E should be negative
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Typical Optimization Formulations
Aero Structures
Efficiency Weight, Pull
Design Variables Objective Function(s) Thickness distribution Chord distribution CG offsets (stacking)
Design Constraints Design point flow pressure profile Off-design lapse Stability Casing clearance Material properties Stress Tuning Flutter
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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

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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 Kts available via Petersons
  or FEA
• Nominal stress
• S-N curve

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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

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Motion of a damped spring-mass system
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Forced motion Damped spring-mass system
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Chinook helicopter
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Airfoil Tuning Represented on Campbell Diagram

• Airfoil frequency vs. rpm
• Excitation orders
• Static flow disturbance relative to the rotating
  frame
• Source inlet distortions
• Freq EORPM/60
• Project Requirements
• 1st bending _at_ RL gt 20
• 2nd 3rd modes _at_ RL gt 5

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HCF Strength Assessed with Goodman Diagram
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Stresses
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Secondary Air Systems
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S
R
S
R
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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)

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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

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Structural Design Considerations

• Airfoil Centrifugal Stress
• Blade of constant cross section has mass

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Turbomachinery DesignStructural Considerations
Centrifugal stress is limited by blade material
properties
Aan
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Turbomachinery DesignStructural Considerations
Centrifugal stress is limited by blade material
properties
L
Cent. bending
Gas bending
From Rear
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Mechanical Design Minimizing Root Moments
Pull
CG
Air pressure

• 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 Offset
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Turbomachinery DesignStructural Considerations

• Bending stress on a cantilevered bead under
  aerodynamic loading Kerrebrock
• Centrifugal stress is typically larger than
  bending stress

c/s?
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Typical Centrifugal Stress Values
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Typical Centrifugal Stress Values
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Typical Centrifugal Stress Values
Need to determine if blade with this stress level
will last 1000hr to rupture
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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

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Turbomachinery DesignStructural 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

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Turbomachinery DesignStructural 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

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Turbomachinery DesignStructural 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 (?)

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Turbomachinery DesignStructural 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)

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

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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)

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Turbomachinery Gaspath Design Problem

• Base Case Assume only for this case M10.8 is
  given.

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Turbomachinery Gaspath Design Problem

• Base Case Assume only for this case M10.8 is
  given.

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Turbomachinery Gaspath Design Problem

• Base Case

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Turbomachinery Gaspath Design Problem

• Base Case

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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)

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Turbomachinery Gaspath Design Problem

• Alternate Design 1 Given N, Aan1N2, Dmean1

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Turbomachinery Gaspath Design Problem

• Alternate Design 1

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Turbomachinery Gaspath Design Problem

• Alternate Design 1

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Turbomachinery Gaspath Design Problem

• Summary