A Computational Efficient Algorithm for the Aerodynamic Response of Non-Straight Blades Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssing

A Computational Efficient Algorithm for the Aerodynamic Response of Winglet Blades Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark Sørensen & Mads Døssing

Mar EWEA 2011, Brussels, Belgium3Risø 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 EWEA 2011, Brussels, Belgium4Risø DTU, Technical University of Denmark Why this Work? The addition of winglets to a wind turbine rotor can increase C P 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 EWEA 2011, Brussels, Belgium5Risø 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 EWEA 2011, Brussels, Belgium6Risø 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: V rel 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

Mar EWEA 2011, Brussels, Belgium7Risø DTU, Technical University of Denmark Prescribed wake model Mimics the behavior of the free wake model using emperically determined wake shape prescription functions (r filament,i /R, filament pitch angle)=f(r filament,i,z=0 /R, C T, Z/R, l wl /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 EWEA 2011, Brussels, Belgium8Risø DTU, Technical University of Denmark Example of Free/Prescribed Wake outputs Inputs –Blade span geometry –Bound vorticity  B –Lift to drag ratio C L /C D Outputs –Induced velocities –Local loadings Optimization can be added to determine the bound vorticity

Mar EWEA 2011, Brussels, Belgium9Risø DTU, Technical University of Denmark Design of (wingletted) rotors using LL results Joukowski Design choices: Blade span geometry Airfoil types  Angle of attack   Lift to drag ratio C L /C D Results from LL optimization: Bound vorticity  B Induced velocities V rel Local loadings Outputs from the design method: Chord distribution Twist distribution

Mar EWEA 2011, Brussels, Belgium10Risø DTU, Technical University of Denmark Design of (wingletted) rotors using LL results Example of how such a design can look: Design from Lifting LineDesign for CFD

Mar EWEA 2011, Brussels, Belgium11Risø 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) C T /C Tref C P /C pref CFD Ellipsys3D3.91%2.15% LLFW2.61%2.47%

Mar EWEA 2011, Brussels, Belgium12Risø DTU, Technical University of Denmark From LL to CFD: Automatic surface meshing Based on python scripts controlling Pointwise 36 blocks of 32 2 cells ~ cells

Mar EWEA 2011, Brussels, Belgium13Risø DTU, Technical University of Denmark From LL to CFD: Automatic 3D meshing Based on Risø DTU’s Hypgrid3D y + <2 540 blocks of 32 3 cells ~17.7M cells

Mar EWEA 2011, Brussels, Belgium14Risø DTU, Technical University of Denmark CFD flow solver: EllipSys3D Finite Volume Method Rotating mesh Multigrid SIMPLE QUICK MultiBlock Steady state k--SST -ReLaminar –turbulent transion Parallelized with MPI Convergence under 12h on 20 CPUs

Mar EWEA 2011, Brussels, Belgium15Risø DTU, Technical University of Denmark CFD results: Surface streamlines (Winglet 8%) Pressure side Suction side No rotational effects! No stall!

Mar EWEA 2011, Brussels, Belgium16Risø DTU, Technical University of Denmark CFD results: Surface streamlines (Winglet 8%) Suction side with vorticity iso-surface and surface pressure color contour

Mar EWEA 2011, Brussels, Belgium17Risø DTU, Technical University of Denmark CFD results: Pressure Coefficient (Winglet 8%) Pressure side Suction side

Mar EWEA 2011, Brussels, Belgium18Risø DTU, Technical University of Denmark CFD results: Extracting pressure distribution

Mar EWEA 2011, Brussels, Belgium19Risø DTU, Technical University of Denmark 80% 40% CFD results: Extracting pressure distribution (Winglet 8%)

Mar EWEA 2011, Brussels, Belgium20Risø DTU, Technical University of Denmark CFD results: Extracting pressure distribution (Winglet 8%) 100% 40%

Mar EWEA 2011, Brussels, Belgium21Risø DTU, Technical University of Denmark Comparison LL & CFD (Winglet 8%)

Mar EWEA 2011, Brussels, Belgium22Risø DTU, Technical University of Denmark Comparison LL & CFD (Winglet 8%) Illustration of total force Non dimensionalized total force

Mar EWEA 2011, Brussels, Belgium23Risø DTU, Technical University of Denmark Comparison LL & CFD (Normal rotor) total force Illustration of total force Non dimensionalized total force

Mar EWEA 2011, Brussels, Belgium24Risø 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 EWEA 2011, Brussels, Belgium25Risø 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 EWEA 2011, Brussels, Belgium26Risø DTU, Technical University of Denmark Thank you for your attention Winglet geometries are available for comparison in open access on