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

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

• Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark
  Sørensen Mads Døssing
• macg_at_risoe.dtu.dk

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A Computational Efficient Algorithm for the
Aerodynamic Response of Winglet Blades

• Mac Gaunaa, Pierre-Elouan Réthoré, Niels Nørmark
  Sørensen Mads Døssing
• macg_at_risoe.dtu.dk

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Contents

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

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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
• gt Possibilities for modelling also other
  non-standard geometries than winglets (swept
  blades, coning, )

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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)

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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 gt trailed
  vorticity bound vorticity difference
• No viscous forces in vortex models. These are
  taken into account separately

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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,z0/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

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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

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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

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Design of (wingletted) rotors using LL results

• Example of how such a design can look

Design from Lifting Line
Design for CFD
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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
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From LL to CFD Automatic surface meshing
Based on python scripts controlling Pointwise
36 blocks of 322 cells 37 000 cells
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From LL to CFD Automatic 3D meshing
Based on Risø DTUs Hypgrid3D
ylt2 540 blocks of 323 cells 17.7M cells
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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

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CFD results Surface streamlines (Winglet 8)
Suction side
Pressure side
No rotational effects! No stall!
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CFD results Surface streamlines (Winglet 8)
Suction side with vorticity iso-surface and
surface pressure color contour
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CFD results Pressure Coefficient (Winglet 8)
Suction side
Pressure side
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CFD results Extracting pressure distribution
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CFD results Extracting pressure distribution
(Winglet 8)
80
40
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CFD results Extracting pressure distribution
(Winglet 8)
100
40
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Comparison LL CFD (Winglet 8)
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Comparison LL CFD (Winglet 8)
Illustration of total force
Non dimensionalized total force
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Comparison LL CFD (Normal rotor)
Illustration of total force
total force
total force
Non dimensionalized total force
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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?
• gt More work to be done to determine the origin
  of this discrepency

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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?

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Thank you for your attention

• Winglet geometries are available for comparison
  in open access on
• http//windenergyresearch.org