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Transcript of 1 Axial Flow Compressors: Efficiency Loss: Centrifugal Compressors Efficiency Loss: Axial Flow...

  • Axial Flow Compressors:Efficiency Loss:

    Centrifugal CompressorsEfficiency Loss:

    Axial Flow turbines:Efficiency Loss:

  • Turbomachinery

    Class 11

  • Configuration Selection & Multidisciplinary Decisions

    Turbomachinery Design Requires Balance Between:

    PerformanceWeightCost

  • Turbomachinery DesignSeveral Aspects to "Cost" as seen by customer

    First Cost - PriceOperating Cost -Fuel & MaintenanceEfficiencyWeightNo. of PartsComplexityManufacturingMaterialsLife; Stress & Temperature

  • Turbomachinery DesignConsider 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 1965Correlation of Rolls Royce data for 70 TurbinesShows shape of velocity diagram is important for turbine efficiencyCorrelation conditions- Cx approximately constant- Mach number - low enough- Reaction - high enough- Zero swirl at nozzle inlet- "Good" airfoil shapes- Corrected to zero clearance

  • Increasing Note: The sign of E should be negative

    Smith Turbine Efficiency Correlation

    94%

    92%

    90%

    88%

    0.8

    1.2

    1.6

    2.0

    2.4

    2.8

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4

    Cx/u

    E

  • DixonThis is E

  • Turbomachinery DesignEfficiency 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!

  • Secondary Air Systems

  • Turbomachinery Design Structural ConsiderationsCentrifugal stresses in rotating componentsRotor airfoil stressesCentrifugal due to blade rotation [cent]Rim web thicknessRotating 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 airfoilsThermal: Stresses arising from radial thermal gradientsCyclic effect called low-cycle fatigue (LCF)

  • Turbomachinery DesignStructural ConsiderationsAirfoil Centrifugal StressBlade of constant cross section has mass:

  • Turbomachinery DesignStructural ConsiderationsCentrifugal stress is limited by blade material propertiesAan

  • Turbomachinery DesignStructural ConsiderationsFor centrifugal stress of 40,000 lbf/in2,AanN2 = 790,000 x 40,000=3.16 x 1010 Design practice for AN2 is from (2.5-3.5) x 1010

    Since N is fixed, this places upper limit on annulus area

    In another, more basic form:

    Where:UtBlade Tip Speed,ft/secmMetal Density, lbm/in3centCentrifugal Stress, lbf/in2l hub/tip radius ratioFrom chart 11

  • Typical Centrifugal Stress Values

    Compressor

    Turbine

    (

    Slugs/ft3

    9.0

    15.0

    N

    RPM

    10,000

    10,000

    A

    ft2

    2.0

    1.0

    AN2

    in2-RPM2

    2.88 x 1010

    1.44 x 1010

    rT/rH

    0.8

    8.8

    (c

    psi

    19,630

    16,360

  • Typical Centrifugal Stress Values

  • Typical Centrifugal Stress ValuesNeed to determine if blade with this stress level will last 1000hr to rupture

  • Turbomachinery DesignStructural ConsiderationsCentrifugal stresses due to torsional disk stressesThe force from the change in angular momentum of gas in the tangential direction which produces useful torque.Mw = bending moment about axial directionMa=gas bending moment about tangential direction [If Cx constant, pressure force produced in axial direction]Mw is largest bending momentApproximate form for bending stress

    Design blade with centroids of cross section slightly off-centergas bending moment is of opposite sign to centrifugal bending moment

  • Turbomachinery DesignStructural ConsiderationsDisk & 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 doesnt exactly match Smith data

  • Turbomachinery DesignStructural ConsiderationsAllowable stress levels are set by material properties, material temperature, time of operation and cycles of strain

    Stress level measuresUltimate stress: part fails if this level is reached1000 hrs rupture life: part fails after 1000 hrs at a given temperature1000 hrs creep life: part will stretch a certain percentage (0.1 - 0.2%) at a given temperature

  • SSRR

  • Turbomachinery DesignStructural 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

  • Turbomachinery DesignStructural ConsiderationsExternal load due to:

    airfoil, attachment & platform pulldisk lugside plates, seals, etc.

    Inertial loads due to:

    centrifugal force from bore to live rim

  • Turbo Design - Structural ConsiderationsAirfoils 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 ConsiderationsAverage Tangential StressConsider radial inertia load on disk element:

    Noting that , an element of area in the disk cross section:

    Tangential disk stresses: forces on itself due to rotation + external (blade pull ) forces

  • Turbomachinery DesignStructural 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:

  • Turbomachinery DesignStructural Considerations

    note that

  • Turbomachinery DesignStructural ConsiderationsThe 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:

  • Turbomachinery DesignStructural ConsiderationsFor 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

  • Turbomachinery DesignStructural ConsiderationsRim Stress - Consider a thin ring. Neglecting the external force, the rim inertial tangential force is:

    Xdrr

  • Turbomachinery DesignStructural ConsiderationsImportant 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

  • High Disk Stress in Advanced HPTs

    1000

    1200

    1400

    1600

    1800

    100

    200

    300

    400

    500

    600

    700

    A*N2 X 10-8

    Rim Speed ft/sec

  • Turbomachinery DesignStructural ConsiderationsAverage Tangential Stress in HPT disks is Increasing

    Engine

    SYMBOL 115 \f "Symbol"External

    ksi

    SYMBOL 115 \f "Symbol"Inertial

    SYMBOL 115 \f "Symbol"Total

    SYMBOL 37 \f "Symbol"

    1982

    32

    68

    100

    32

    1980

    43

    70

    113

    38

    2000

    52

    62

    114

    46

    2010

    46

    64

    110

    42

    2015

    54

    71

    125

    43

  • Turbomachinery DesignStructural ConsiderationsConclusions:

    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

  • Turbomachinery DesignStructural ConsiderationsStress 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 ()

  • Turbomachinery DesignStructural ConsiderationsAlso :

    Flow, Density & Work are set by cycle requirements

    Stress (P/A) capability is set by material, temperature, & blade configuration

    Parametric effectsincreased N increased (to first order), decreased E (to 2nd order)increased D decreased (to first order), decreased E (to 2nd order)

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

  • Turbomachinery Gaspath Design ProblemObjective: to illustrate interaction of several design parameters, stress level (cent), x, cost, weight flowpath dimensionsDesign a baseline turbine and 3 alternative configurationsDmean or weight and cost on Aan or Cx or weight on Stress level on All turbine designs have the following conditions

  • Turbomachinery Gaspath Design ProblemDesign: fill in the missing