*Turbomachinery

Class 8a

*Axial Flow Turbomachine DesignThree-dimensional flow through machine very complex

Decompose problem into series of two-dimensional problemsBlade-to-blade [Cascade] (x, y=)Plane cascade (no spanwise effect)Stream surface (span effect modeled within 2D constructThrough flow [Meanline] (r, x)Blades modeled as thin or actuator discsSecondary flow [normal to mainstream] (r, )

Design problem largely treated as inviscid analysis with viscous effects accounted for through empirical and semi-empirical methods

*Airfoil/Cascade DesignCascade - array of airfoils providing forces that change flow vectors.

Requirements:

Produce required forcesLow total pressure lossWide range of low loss incidence: operate at off-design pointsStable exit angles

Turning should be produced so that losses are minimum

Airfoils [compressors] typically selected from family or series of airfoils

*Geometry of a Rectilinear Cascade Geometry Parameters

SolidityStagger angle: angle between chord line and leading edge front of cascadeCamber / TurningMaximum thicknessLeading edge / trailing edge thickness / radiusUncovered turning

*Airfoil NomenclatureChord: c or b = xTE-xLE; straight line connecting leading edge and trailing edge

Camber line: locus of points halfway between upper and lower surface, as measured perpendicular to mean camber line itself

Camber: maximum distance between mean camber lineand chord line

Thickness t(x), tmax

Angle of attack: , angle between freestream velocity and chord line

*Geometry of a Rectilinear Cascade

*Geometry of a Rectilinear Cascade

*Compressor Airfoil DesignCompressor Airfoil Series - geometric families

Circular arc (CA): for high Mach number flowsmean camber line is circular arc with max camber and max thickness at 50%c

65-series for moderate subsonic Mach numbersmean camber line is a parabola with max camber at 50%c and max thickness at 40%c

400-series for low Mach numbersmax camber at 40%c and max thickness at 30%cthickness distribution NACA SP-36 p.198 or Abbot and Von Doenhoff

*Compressor Airfoil Design

*Compressor Airfoil DesignCompressor Airfoil Series - geometric families

Initially developed from wing dataUsed through 1970'sLarge bodies of cascade data NASA, P&W, UTRC, DFVLR, NGTE, ONERALoss & flow turning = f (incidence, Mach no., area ratio & geometry)Experimental Data Verifies Design Codes

*Airfoil/Cascade PerformanceShear layer development over solid surface

*Airfoil/Cascade PerformanceFriction effects can adversely affect cascade performance

*Airfoil/Cascade PerformanceBoundary layer thickness assessment parameters:* = displacement thickness = momentum thicknessH = shape factor = * / (1< H < 2.2)

Equal mass =

*Airfoil/Cascade PerformanceBoundary layer thickness assessment parameters:* = displacement thicknessHowell correlation

*Airfoil - Cascade Comparisons Observations

Cd dependence on Mach is small until critical McrCl dependence on Mach is strongShocks & shock boundary layer interaction lead to flow separation, lift loss, drag riseIsolated Wing Lift-Drag Curve

*Airfoil - Cascade ComparisonsM>1M

*Airfoil - Cascade ComparisonsPlane Cascade Lift-Drag Curve Lift Circulation ( ) turning deflection

Drag total pressure change loss What observations can you make about these curves?Dixon Howell [1942]

Loss Bucket

*Minimum loss incidence rangeChokeStall

*Limits of Compressor Cascade OperationStallAnalogous to wing stallHigh positive incidence, separation from suction sideLoss & Deviation (difference between flow and exit camber angles) rising rapidly, work & efficiency fall

ChokePressure surface separation due to negative incidenceActual choke: not enough area at throat to pass mass flowChoke margin decreases as flow becomes more axial (M=const)

*

*Low pressure, high Mach number [suction side]High pressure, low Mach number [pressure side]% chordT.E. Kutta conditionAirfoil/Cascade Design Airfoil shapes constructed to have desirable surface pressure distributions and boundary layer characteristics

Airfoil shapes must also meet structural criteriaAdversegradient

*Design for Lift, Min Loss, Max Range & Choke MarginAvoid flow reversalIdealAvoid separationAvoid leadingedge sep. bubbleCan also view this in terms of ps/p0

*Airfoil/Cascade DesignCascade Testing:

Vital Requirements

Periodicity

Endwall boundary layer control

Uniform flow

Accurate pitch-wise Traverse data

*Additional Factors:AVDR - Axial Velocity - Density Ratio - area ratio due to end wall boundary layer growth [Geometry 2D but flow 3D] Effects deviation[ ]

Compressor Airfoil/Cascade DesignContraction of streamlines due to boundary layer thickening

*Compressor Airfoil/Cascade PerformanceBackground: Boundary layer thickness parameters: = momentum thickness* = displacement thicknessH = shape factor = * / (1< H < 2.2)

*Compressor Airfoil/Cascade PerformanceLoss Analysis - Lieblein's Dfactor [Diffusion Factor]

Momentum Integral Equation describes the growth of boundary layer thickness along the suction surface:

where:V = relative velocity at edge of boundary layer

x = distance along airfoil surface

- Boundary layer eqns.- Integrate y: 0 to Boundary layer PDE integrated over y from 0 to

*Lieblien's insight:

Correlation of cascade pressure distribution data for constant radius:

Velocities are in Relative Frame [V=W]. Solidity =b/s. The 2 is empirical [from cascade data].Now to connect Df to loss...Compressor Airfoil/Cascade PerformanceVsurfVmaximumV(x)V2

*Wake Momentum Thickness vs. Calculated DiffusionEmpirical relation [Leiblien] connecting /c (or loss) to Df

*Compressor Airfoil/Cascade PerformanceUses of Dfactor Today

- Preliminary design surge margin limit for known clearance & aspect ratio

- Low speed loss prediction in mean line systems

0 < Dfactor < 0.7

- Given loss [ /c ], now find loss coefficient [ ]

ExampleA compressor rotor with the following conditions:U=200 mpsCx1=Cx2=150 mps2=35 degs.

Calculate W1, W2, Df

*

*Loss Coefficient Directly Related to Wake Momentum Thickness Ratio, /c

*Relation Between /c and [Extra]Empirical expression

*What is the Impact of D-factor on Airfoil ShapeCarters Rule for compressor cascades

For HWK 6.3, since =1

Metal angle decreases to achieve design exit angle goals

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*Compressor Airfoil/Cascade Performance

Compressor Airfoil Performance

Dfactor sets Wake Thickness

Wake Thickness and # Wakes sets Loss Coefficient

Loss Coefficient and Work Coefficient sets Efficiency

*Turbomachinery

Class 8b

*Overview of Loss Analysis - Lieblein's DfactorCorrelation of cascade data [Velocities in Relative Frame]

or de Haller [ 0.72

*High deflection compressor airfoil [reducing 2 with fixed 1] means reducing V2.Early diffusion based design method by de Haller called for 0.72

*Repeating stage, repeating row [mirror image airfoil]

Compressor Airfoil/Cascade Performance

*Dfactor analysis for repeating row stage

Compressor Airfoil/Cascade Performance

*Airfoil/Cascade PerformanceAirfoil Sections Now Designed to Pressure DistributionsCompressible Potential flow code for local M

*Compressor Airfoil/Cascade DesignControlled Diffusion Airfoils (CDA @P&W, CTA @ GE)

Higher peak Mach no., tapered dV/dx

More camber in front half of chord

Elliptical Leading edges

Stall range assured by gradual initial acceleration

Not optimum at end walls

*Turbine Airfoil/Cascade DesignTurbine Airfoil Design

Historically more Analytical than Compressors

Accelerating Flow...Probably the ReasonBoundary layer separation easier to avoid

Design to Pressure Distributions

Correct for deviation effects

Zweifel Load Coefficient & Convergence

Desirable Pressure Distributions

*Turbine Rotor 2 3Constant Cx, no exit swirl [3=0]High loading stage [E

*Turbine Rotor 2 3For repeating row design and no exit swirl E=2[R-1]

*Cascade Design ProblemPressure sideSuction sideExitPressureGoodPoor- toomuch diffusion Desirable pressure distributions

*What is the Impact of Deviation on Airfoil ShapeCarters Rule for turbine cascades

Metal angle decreased to achieve design exit angle goalsEffect for turbine is much smaller for turbines due to thinner boundary layers

*Zweifel Coefficient DerivationArea FidealArea FSolidity issue: Enough airfoils must be used so that F = change in tangential momentum of the fluid.Solidity play important role in turbine efficiency: (1) spacing small, fluid getsmaximum turning force with large wall friction forces; (2) spacing large, fluidgets small turning force with small wall friction losses.

*Zweifel Coefficient Derivation

*Turbine Airfoil/Cascade DesignZweifel Load Coefficient:

where bx is the axial chord and h is the streamtube spanwise width and x = bx / s

Treating the pressure difference incompressibly:

*Turbine Airfoil/Cascade DesignSimplifying:

Zweifel Coefficient: 1st estimate of solidity.

*Turbine Airfoil/Cascade DesignZweifel Coefficient: 1st estimate of solidity.

Zweifel noted that turbine min.loss for z 0.8. Optimumspacing estimated from giveninlet and outlet angles.

*Turbine Airfoil/Cascade DesignZweifel Coefficient: 1st estimate of solidity.

Other Factors:Pressure Distributions

CoolingResonances Disk StressWeightCost

Some of this covered aftermeanline analysis

*Turbine Airfoil/Cascade DesignTurbine Airfoil Design Approach [covered in following charts]

Balance Acceleration & Diffusion

Use Laminar Boundary layer where possible

Diffuse with Turbulent Boundary layer

Control Maximum Mach No. & Shocks

Control Leading Edge Overspeed

Manage Uncovered Turning

*Turbine Airfoil/Cascade Design Balance Front End Acceleration With Rear DiffusionLaminar boundary layers on suction surface reduces losses on front, turbulent boundary layers on rear more tolerant to flow separation.

* More BladesIncreases Solidity [ = b/s]Reduces Force per Blade

*Aft Curvature Moves Loading Aft

*Turbine Airfoil/Cascade DesignHigh Convergence Eases Cascade Design

Like an area ratio: Aan is an annulus area

Convergence is Function of Velocity Diagrams, not airfoil shape

High Reaction = higher blade convergence

*Turbine Airfoil/Cascade Design

*Turbine Airfoil/Cascade DesignThin Edges are best for Aerodynamic PerformanceTrailing Edge Blockage Drives Base DragTET = Trailing Edge Thickness

Stewarts mixing loss correlation is function of TET and *s.s. , *p.s.Casting capability, stress & cooling set minimum edge thicknessHigh wedge angle eases effect at leading edge

Elliptical LE is betterPressure Distribution Improved; Overspeed reduced in both surfaces

*Turbine Airfoil/Cascade Design Manage Uncovered TurningThroatTransonic Flow:More uncovered turninglowers base pressure loss(

*Consequences of Stagnation Point Location

*Turbine Airfoil/Cascade Design Manage Uncovered TurningUncovered turning is less of an issue for subsonic turbine airfoils

*Thermo & Kinematic View of Compressor StageNote: U>C

*Thermo & Kinematic View of Turbine StageNote: U

*Thermo & Kinematic View of Turbine Stage

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