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Aeroelastic modelling of vertical axis wind turbines
Aagaard Madsen , Helge; Larsen, Torben J.; Schmidt Paulsen, Uwe; Kragh, Knud Abildgaard
Publication date:2013
Link back to DTU Orbit
Citation (APA):Aagaard Madsen , H. (Author), Larsen, T. J. (Author), Schmidt Paulsen, U. (Author), & Kragh, K. A. (Author).(2013). Aeroelastic modelling of vertical axis wind turbines. Sound/Visual production (digital)
https://orbit.dtu.dk/en/publications/14b62044-d3e7-4e70-a6d7-6c18434e56ba
Aeroelastic modelling of vertical axis wind turbines
Helge Aagaard Madsen Torben Juul Larsen Uwe Schmidt Paulsen Knud Abildgaard Kragh Section Aeroelastic Design Department of Wind Energy hama@dtu.dk
mailto:hama@dtu.dk
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Credits Image by Grimshaw & Wind Power Ltd
Renewed interest in Vertical Axis Wind Turbines - Most floating MW concepts
DeepWind 5MW design
2
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Small on-shore Vertical Axis Wind Turbines
http://www.windpowertree.com/products.html
Windpower tree
http://windpowerdirectory.net/manufacturers/vawt/quiet-revolution-s14.html
Quiet revolution
http://windpowerdirectory.net/manufacturers/vawt/wepower-creating-and-delivering-clean-energy-solutions-s41.html
3
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Accurate aerodynamic and aeroelastic design tools are necessary for the design studies of new VAWT concepts
Aeroelastic code HAWC2 – Horizontal Axis Wind Turbine Code
?
4
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
HAWC2 – developed from 2003-2006 at DTU Wind (former Risø)
Structural core based on a multibody formulation Joints modeled by geometric constraints
Use for VAWT´s ? Arbitrary geometry √ Hydrodynamic loads √ Wave loads √ Mooring lines √ Turbulent inflow model √ Aerodynamic blade loads √ Dynamic stall √
BEM induction model ÷ Magnus forces on floater ÷
HAWC2
5
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Induction model implemented The Actuator Cylinder (AC) flow model
Swept surface a cylinder
Blade forces distributed on the cylinder surface
- an extension of the actuator disc AD concept to an actuator cylinder
6
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
The AC flow model – the loading
Blade forces distributed on the cylinder surface:
Where and are the projections of the lift and drag blade forces on a direction normal to chord and tangential to the chord
( )θnF ( )θtF
( ) ( ) ( ) ( ) ( )22sincos
∞
−=
VRFF
BQ tnn ρπϕθϕθ
θ
( ) ( ) ( ) ( ) ( )22coscos
∞
+−=
VRFFBQ ntt ρπ
ϕϕϕθθ
7
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
How to compute the flow field for the AC model ?
8
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
yyxx wvandwv =+= 1
1) a standard CFD code can be used:
( ) ( )drfQs
snn ∫
∆
∆−
= θθ
( ) ( )drfQs
stt ∫
∆
∆−
= θθ
2) a solution procedure with potentials for low computational demands:
Approach: solution is split into a linear and a non-linear part
Velocity components are written as:
Equations non-dimensionalized with: , , ∞V ρ R
9
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
The Linear solution
Assuming the loading is constant within an interval θ∆
( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( ) ( )( )
θθθ
θθθθθθ
θθ
djyjxjyjxjiR
i
i
xw ∫∆+
∆− −++−++−
=½
½22 cossincoscossinsin,
The influence coefficients can be computed once for all:
( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( ) ( )( )
θθθ
θθθθθθ
θθ
djyjxjyjxjiR
i
i
yw ∫∆+
∆− −++−−+−
=½
½22 cossinsincoscossin,
( ) ( ) 36.....2,1½cos =∆−∆−= jjjx ϕϕ ( ) ( ) 36........2,1½sin =∆−∆= jjjy ϕϕ
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( ) ( ) * )(,*,1
, ,21
jNnjnw
Ni
iinx QQjiRQjw x −
=
=
+−= ∑π
( ) ( )∑=
=
=Ni
iwiny jiRQjw y
1, ,2
1π
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results
RcB
2=σSolidity
11
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results – flow
12
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
A modified linear AC model
*112
1 px
yarctgx
yarctgpvx ∆−
++
−∆−=
π
( )( )
−+
++∆= 22
22
11ln
4 yxyxpvy π
The same method of solution (linear and non-linear part) is used for the 2D actuator disc:
linT aC 4=
However, from BEM theory we have:
244 aaCT −=
To achieve a modified linear solution we multiply the inductions with the factor
aka −
=1
1
13
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results – modified linear AC model
14
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results – modified linear AC model
15
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results
rotor radius 60.51m blade chord 5.0m rotor height 143.0m airfoil NACA0018 number of blades 2 solidity 0.17 rated power 5000kW rated speed 5.63rpm swept area 12318m2
16
- 5MW DeepWind 2nd design Baseline design
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results –from baseline to 2nd design
17
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results -5MW baseline DeepWind design
18
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Results -5MW baseline DeepWind design
19
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Conclusions
The aeroelastic model HAWC2 has been extended to model VAWT´s with the same level of accuracy as HAWT´s
Experience on aeroelastic modelling of VAWT´s is being build up at the moment
20
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Acknowledgement
The DeepWind project is supported by the European Commission, Grant 256769 FP7 Energy 2010- Future emerging technologies:
Participants DTU Wind (DK) AAU(DK) TU DELFT(NL) TRENTO Univ. (I) DHI(DK) SINTEF(N) MARINTEK(N) MARIN(NL) NREL(USA) STATOIL(N) VESTAS(DK) NENUPHAR(F)
21
DTU Wind Energy, Technical University of Denmark
Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen
Thank you for your attention
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