Aeroelastic modelling of vertical axis wind turbines...Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen HAWC2 – developed from 2003-2006 at DTU Wind (former Risø) Structural

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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 [email protected]

mailto:[email protected]

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



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



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



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



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



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



How to compute the flow field for the AC model ?

8



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



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

10

( ) ( ) * )(,*,1

, ,21

jNnjnw

Ni

iinx QQjiRQjw x −

=

=

+−= ∑π

( ) ( )∑=

=

=Ni

iwiny jiRQjw y

1, ,2

1π



Results

RcB

2=σSolidity

11



Results – flow

12



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



Results – modified linear AC model

14



Results – modified linear AC model

15



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



Results –from baseline to 2nd design

17



Results -5MW baseline DeepWind design

18



Results -5MW baseline DeepWind design

19



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



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



Thank you for your attention

22

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Documents

Aeroelastic modelling of vertical axis wind turbines...Danish Wind Power Research 2013, May 27-28 2013, HAa Madsen HAWC2 – developed from 2003-2006 at DTU Wind (former Risø) Structural