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

date post

05-Jan-2016Category

## Documents

view

216download

2

Embed Size (px)

### 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

Recommended

*View more*