Siemens Wind Power - Wind Energywindpower.sandia.gov/2008BladeWorkshop/PDFs/Tues-06-Hjort.pdf · Siemens Power Generation 2005. All Rights Reserved Siemens Wind Power Aerodynamic

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Siemens Wind Power

Aerodynamic Winglet Optimization

Author: Søren Hjort

Co-authors: Jesper Laursen, Peder Enevoldsen

Siemens Wind Power

Structural Dynamics, aerodynamic dept.

2007-05-08 Power Generation 2Siemens Wind Power

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SANDIA BLADE WORKSHOP 2008

Presentation outline

Problem statement

Model

Validation and results

Conclusions

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Problem statement

Today’s engineering workhorse for blade/rotor design is the Blade-Element-Momentum (BEM) method.

Straight slender blades:

BEM Very applicable in combination with well-known model add-ons (tip-loss correction, dynamic inflow, 3D-correction, stall-hysteresis …)

Arbitrary geometry slender blades:

BEM fundamentally inapplicable due to break-down of the radial independency assumption.

Examples are: Winglets, large cone angles, large edge- and/orflap-wise pre-deflection.

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Model

Objective:

To develop a fast “engineering” induction model for arbitrarily shaped slender blades

• Mesher

• CFD Actuator Disc solver

• Vortex-line method

• Large DOF optimization

Model components:

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Aircraft winglet examples:


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The mesher

• Curvi-linear structured 2D quad mesher.

• Algorithm : Advancing front.

−400 −300 −200 −100 0 100 200 300 400−100

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Axial distance [m]

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256 x 224 domain

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Axial distance [m]

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256 x 224 domain (close−up)

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Axial distance [m]

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256 x 224 domain (close−up)

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The CFD Actuator Disc solver

Governing equations: 2D incompressible Navier-Stokes, cylindrical frameFormulation: Curvilinear finite volumeAlgorithm: SIMPLE with full multi-grid accelerationActuator disc (rotor) represented as volume forces over the disc domain.

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Velocity magnitude iso−lines [3.3 ; 11.8] m/s

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The vortex-line method

0 50 100 150 200−50050

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Tip− and root−vortex from 1 bladePropagate shed vorticity

along streamlines from the

CFD Actuator Disc solution.

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The vortex line method

Assumption : Complete flowfield described by rotating blade induced vortex lines:

• Bound vorticity lines along the blades.• Vorticity lines shed from the blades. The shed vorticity is convected by

the flowfield computed by the actuator disc CFD solver.

Integration of flowfield along one blade (symmetry) using Biot-Savart’s law for a linear vortex filament is summed by 3 integrated/calculated quantities:

• Bound vorticity from all blades (filament integration).• Shed vorticity from all blades. Truncation at farfield 5 rotor diameters

downstream (filament integration).• Farfield residual induction from 5 D to infinity (vortex tube semi-

analytical integrals)

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Large DOF optimization

Combined line-search / quasi-Newton bounded optimization for large systems.

“Quasi” : Hessian matrix is only computed for the diagonal elements. Off-diagonal elements are estimated => computational efficiency

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Validation of CFD Actuator Disc solver

Err.Act.DiscXbladeRotorWind(BEM code)rpmspeed

0.3 %1945193916.0 rpm10 m/s

-0.3 %1006100913.5 rpm8 m/s

-0.2 %42342410.0 rpm6 m/s

Comparison of mechanical power [kW] from an SWT-2.3-93 :

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Validation of the Vortex-line method

SWT-2.3-93Field measurements from an SWT-2.3-93 at Høvsøre National Test Site, Denmark

Rotor computation of an SWT-2.3-93:

Solver: Ansys CFX

Equations: steady RANS

Formulation: Finite volume

Turb. Model: SST

Mesh: Block hexahedra

Size: ~4 mio. elements

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Validation of the Vortex-line method

Vortex lineANSYS-CFXFieldRotorWind

/ Ellipsysmeasurementrpmspeed

18971853/1853189416.0 rpm10 m/s

982950/94598613.5 rpm8 m/s

413396/39240010.0 rpm6 m/s

Comparison of mechanical power [kW] from an SWT-2.3-93, measured or computed by 3 different methods :

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Results : Testcase 1

Straight blade optimization

Chord : Optimizable, entire span : 33 DOFs

Edge-deflection : Fixed zero : 0 DOFs

Flap-deflection : Fixed zero : 0 DOFs

No. blades : 3

Const. lift coeff. : 1.0

Const. drag coeff. : 0.01

Chord constraint : 3.5 m

Tip radius : 46.2

Free wind : 10 m/s

Rotational velocity : 16 rpm

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4BEM − optimized chord distribution

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rotor radius [m]

mec

h. c

p

Act.Disc. : Cp = 0.5169Act.Disc. no drag: Cp = 0.5610BEM no drag: Cp = 0.5581Betz limit: Cp = 0.5926

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Edgewise winglet optimization

Chord : Fixed from testcase 1 : 0 DOFs

Edge-deflection : Optimizable, outer 2.5m : 16 DOFs

Flap-deflection : Fixed zero : 0 DOFs

No. blades : 3




Tip radius : 46.2

Free wind : 10 m/s


Cp gain: 1.1 %

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Edge−wise winglet geometry

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Flapwise winglet optimization


Edge-deflection : Fixed zero : 0 DOFs

Flap-deflection : Optimizable, outer 2.5m : 16 DOFs

No. blades : 3




Tip radius : 46.2

Free wind : 10 m/s


Cp gain: 2.6 %

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Static pressure iso−lines

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Combined edgewise/flapwise winglet optimization


Edge-deflection : Optimizable, outer 2.5m : 16 DOFs

Flap-deflection : Optimizable, outer 2.5m : 16 DOFs

No. blades : 3




Tip radius : 46.2

Free wind : 10 m/s


Cp gain: > (1.1+2.6) %

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Velocity magnitude iso−lines

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Conclusions

• Flap-wise square-angled winglets (small curvature radius) are optimal when combined with edge-wise deflection. If zero edge-wise deflection, a much larger curvature radius is optimal.

• Edge-wise winglets are optimal when linearly swept backwards.

• The combined flap-wise and edge-wise winglet will increase Cp more than the sum of the isolated flap-/edge-wise Cp gains. However, vortex interactions not accounted for by the model comeinto play here …

For the Cp-optimized straight blade we conclude:

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Thank you for your attention

Documents

Siemens Wind Power - Wind Energywindpower.sandia.gov/2008BladeWorkshop/PDFs/Tues-06-Hjort.pdf · Siemens Power Generation 2005. All Rights Reserved Siemens Wind Power Aerodynamic