A Computational Efficient Algorithm for the Aerodynamic Response of Non-Straight Blades

Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssingmacg@risoe.dtu.dk

A Computational Efficient Algorithm for the Aerodynamic Response of Winglet Blades

Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssingmacg@risoe.dtu.dk

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 3 Risø DTU, Technical University of Denmark

Contents

• Introduction• Basic Winglet Theory• Free/Prescribed Wake Vortex / Lifting Line (LL)• Design of Winglet Rotor• CFD Analysis• Comparison of LL & CFD

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 4 Risø DTU, Technical University of Denmark

Why this Work?• The addition of winglets to a wind turbine rotor can increase CP

• There are commercially available wind turbines with winglets

• No ”computationally light” models are available for aerodynamic prediction of ”non-straight” rotor blades

• We want a physically ”correct” modelling• And results close to much heavier models• => Possibilities for modelling also other non-standard geometries

than winglets (swept blades, coning, …)

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 5 Risø DTU, Technical University of Denmark

Simple Vortex Tube Analysis.

• General result: • Downwind winglet: Higher power on main wing, negative

power on winglet• Upwind winglet: Lower power on main wing, positive power

on winglet• Both cases have the same power production, which is

exactly the same as for the non-wingletted rotor.

• Main difference between a real rotor and this ideal case: • Tip effects and viscous drag

• The trick is to design the winglets such that the benefits from reduction of tip effects outweigh the added viscous drag due to the added surface. (and still no chance of breaking Betz’ limit…)

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 6 Risø DTU, Technical University of Denmark

Vortex Free-Wake Modeling Basics

• Induced velocity due to vorticity. Biot-Savart equation

• The force on a vortex element

OBS: Vrel from rotation, freestream, wake & self-induction!

• In free-wake methods, the wake is force-free, which implies that the wake vortices moves with the flow locally ( )

• Vortices in 3D form closed loops => trailed vorticity = bound vorticity difference

• No viscous forces in vortex models. These are taken into account separately

34 R

RsdVi

relVF

0

relVF

rel

rel

d

l

Boundrel

BoundrelV

V

CC

VVF

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 7 Risø DTU, Technical University of Denmark

Prescribed wake model• Mimics the behavior of the free wake model using emperically

determined wake shape prescription functions(rfilament,i/R, filament pitch angle)=f(rfilament,i,z=0/R, CT, Z/R, lwl/R, )

• Effects included in the model:– Wake expansion (function of both origin radius and axial

coordinate)– Radial and axial velocities connected through continuity– Faster axial convection of wake filaments in the region closest to

maximum radius (outer 10% radii)– Tangential induction from vortex tube theory

• More than two orders of magnitude faster than free wake model• Results close to free wake results. Very close if the shape of bound

circulation is close to the ones the prescription function was tuned to.• A detailled description of the model can be found in the paper

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 8 Risø DTU, Technical University of Denmark

Example of Free/Prescribed Wake outputs• Inputs

– Blade span geometry

– Bound vorticity B

– Lift to drag ratio CL/CD

• Outputs– Induced velocities– Local loadings

• Optimization can be added to determine the bound vorticity

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 9 Risø DTU, Technical University of Denmark

Design of (wingletted) rotors using LL results

LiftVF Brel

Joukowski

• Design choices:

• Blade span geometry

• Airfoil types

Angle of attack

Lift to drag ratio CL/CD

• Results from LL optimization:

• Bound vorticity B

• Induced velocities Vrel

• Local loadings

• Outputs from the design method:

• Chord distribution

• Twist distribution

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 10 Risø DTU, Technical University of Denmark

Design of (wingletted) rotors using LL results• Example of how such a design can look:

Design from Lifting Line Design for CFD

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 11 Risø DTU, Technical University of Denmark

Previous work on Free Wake Simulation vs CFD

• Comparison with CFD data for aerodynamically optimal rotor(Johansen et.al J.WE. 2009(12))

• Comparison of increase in CP and CT with the addition of a 2% winglet (Gaunaa et.al. AIAA conference proc., 2008)

CT/CTref CP/Cpref

CFD Ellipsys3D 3.91% 2.15%

LLFW 2.61% 2.47%

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 12 Risø DTU, Technical University of Denmark

From LL to CFD: Automatic surface meshingBased on python scripts controlling Pointwise

36 blocks of 322 cells

~ 37 000 cells

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 13 Risø DTU, Technical University of Denmark

From LL to CFD: Automatic 3D meshingBased on Risø DTU’s Hypgrid3D

y+<2

540 blocks of 323 cells

~17.7M cells

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 14 Risø DTU, Technical University of Denmark

CFD flow solver: EllipSys3D

• Finite Volume Method

• Rotating mesh

• Multigrid

• SIMPLE

• QUICK

• MultiBlock

• Steady state k--SST

• -ReLaminar –turbulent transion

• Parallelized with MPI

• Convergence under 12h on 20 CPUs

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 15 Risø DTU, Technical University of Denmark

CFD results: Surface streamlines (Winglet 8%)

Pressure side

Suction side

No rotational effects! No stall!

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 16 Risø DTU, Technical University of Denmark

CFD results: Surface streamlines (Winglet 8%)

Suction side with vorticity iso-surface and surface pressure color contour

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 17 Risø DTU, Technical University of Denmark

CFD results: Pressure Coefficient (Winglet 8%)

Pressure side

Suction side

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 18 Risø DTU, Technical University of Denmark

CFD results: Extracting pressure distribution

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 19 Risø DTU, Technical University of Denmark

80%

40%

CFD results: Extracting pressure distribution (Winglet 8%)

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 20 Risø DTU, Technical University of Denmark

CFD results: Extracting pressure distribution (Winglet 8%)

100%

40%

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 21 Risø DTU, Technical University of Denmark

Comparison LL & CFD (Winglet 8%)

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 22 Risø DTU, Technical University of Denmark

Comparison LL & CFD (Winglet 8%)

Illustration of total forceN

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imensi

onaliz

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ota

l fo

rce

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 23 Risø DTU, Technical University of Denmark

Comparison LL & CFD (Normal rotor)

total forceto

tal fo

rce

Illustration of total forceN

on d

imensi

onaliz

ed t

ota

l fo

rce

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 24 Risø DTU, Technical University of Denmark

So why this difference?• 3D airfoil characteristics on the curvy part of the winglet?• Self-induced velocities due to interaction between winglet and the main part of

the blade bound-vorticity?=> More work to be done to determine the origin of this discrepency

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 25 Risø DTU, Technical University of Denmark

Outlook, Perspectives & Further work• We have developed a fast and accurate non-straight blade wind turbine code

that can be used to design rotor• It compares relatively well with heavier models

• We are trying to solve the ”winglet lifting-line mystery”• Open questions for future work: How to deal with unsteadiness, shear, yaw,…

in a ”good way”• ... Suggestions?

Mar. 14-17. 2011EWEA 2011, Brussels, Belgium 26 Risø DTU, Technical University of Denmark

Thank you for your attention• Winglet geometries are available for comparison in open access on

http://windenergyresearch.org