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

1. A Computational Efficient Algorithm for the Aerodynamic Response of Non-Straight Blades Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssing macg@risoe.dtu.dk

2. A Computational Efficient Algorithm for the Aerodynamic Response of Winglet Blades Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssing macg@risoe.dtu.dk

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

4. 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, …)

5. 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…)

6. Vortex Free-Wake Modeling Basics • Inducedvelocity due to vorticity. Biot-Savartequation • 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 => trailedvorticity = boundvorticity difference • Noviscous forces in vortex models. Thesearetakenintoaccountseparately

7. 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

8. Example of Free/Prescribed Wake outputs Inputs Blade span geometry Bound vorticity GB Lift to drag ratio CL/CD Outputs Induced velocities Local loadings Optimization can be added to determine the bound vorticity

9. Design of (wingletted) rotors using LL results • Design choices: • Blade span geometry • Airfoil types • Angle of attack a • Lift to drag ratio CL/CD • Results from LL optimization: • Bound vorticity GB • Induced velocities Vrel • Local loadings Joukowski • Outputs from the design method: • Chord distribution • Twist distribution

10. Design of (wingletted) rotors using LL results Example of how such a design can look: Design from Lifting Line Design for CFD

11. Previous work on Free Wake Simulation vs CFD • Comparisonwith 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)

12. From LL to CFD: Automatic surface meshing Based on python scripts controlling Pointwise 36 blocks of 322 cells ~ 37 000 cells

13. From LL to CFD: Automatic 3D meshing Based on Risø DTU’s Hypgrid3D y+<2 540 blocks of 323 cells ~17.7M cells

14. CFD flow solver: EllipSys3D • Finite Volume Method • Rotating mesh • Multigrid • SIMPLE • QUICK • MultiBlock • Steady state k-w-SST • g-Req Laminar –turbulent transion • Parallelized with MPI • Convergence under 12h on 20 CPUs

15. CFD results: Surface streamlines (Winglet 8%) Suction side Pressure side No rotational effects! No stall!

16. CFD results: Surface streamlines (Winglet 8%) Suction side with vorticity iso-surface and surface pressure color contour

17. CFD results: Pressure Coefficient (Winglet 8%) Suction side Pressure side

18. CFD results: Extracting pressure distribution

19. CFD results: Extracting pressure distribution (Winglet 8%) 80% 40%

20. CFD results: Extracting pressure distribution (Winglet 8%) 100% 40%

21. Comparison LL & CFD (Winglet 8%)

22. Comparison LL & CFD (Winglet 8%) Illustration of total force Non dimensionalized total force

23. Comparison LL & CFD (Normal rotor) Illustration of total force total force total force Non dimensionalized total force

24. 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

25. 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?

26. Thank you for your attention Winglet geometries are available for comparison in open access on http://windenergyresearch.org