Aeroelastic modelling of vertical axis wind turbines

Transcription

1 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

2 Renewed interest in Vertical Axis Wind Turbines - Most floating MW concepts DeepWind 5MW design Credits Image by Grimshaw & Wind Power Ltd Danish Wind Power Research 013, May , HAa Madsen

3 Small on-shore Vertical Axis Wind Turbines Windpower tree Quiet revolution tree.com/products.htm l t/quiet-revolution-s14.html facturers/vawt/wepower-creatingand-delivering-clean-energysolutions-s41.html 3 Danish Wind Power Research 013, May , HAa Madsen

4 Accurate aerodynamic and aeroelastic design tools are necessary for the design studies of new VAWT concepts Aeroelastic code HAWC Horizontal Axis Wind Turbine Code? 4 Danish Wind Power Research 013, May , HAa Madsen

5 HAWC developed from at DTU Wind (former Risø) HAWC 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 5 Danish Wind Power Research 013, May , HAa Madsen

6 Induction model implemented The Actuator Cylinder (AC) flow model - an extension of the actuator disc AD concept to an actuator cylinder Swept surface a cylinder Blade forces distributed on the cylinder surface 6 Danish Wind Power Research 013, May , HAa Madsen

7 The AC flow model the loading Blade forces distributed on the cylinder surface: Q Q n t ( θ ) ( θ ) = = B F n Ft B ( θ ) cos( ϕ) F ( θ ) sin( ϕ) π R ρv t ( θ ) cos( ϕ) + F ( ϕ) cos( ϕ) π R ρv n F ( ) ( ) Where n θ and F t θ are the projections of the lift and drag blade forces on a direction normal to chord and tangential to the chord 7 Danish Wind Power Research 013, May , HAa Madsen

8 How to compute the flow field for the AC model? 8 Danish Wind Power Research 013, May , HAa Madsen

9 1) a standard CFD code can be used: Q n Q t s ( θ ) = f ( θ )dr n s s ( θ ) = f ( θ )dr t s ) 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: v = 1 + w and v = x x y w y Equations non-dimensionalized with: V,, ρ R 9 Danish Wind Power Research 013, May , HAa Madsen

10 The Linear solution Assuming the loading is constant within an interval θ x w w The influence coefficients can be computed once for all: R R x y w w * * ( j) Q R ( i j) Q + Q x y ( i, j) ( i, j) 1 = π 1 π = = θ + ½ θ i θ ½ θ i θ + ½ θ i θ ½ θ i i= N i= 1 i = N i= 1 n, i w, ( j) = Q R ( i j) x n, i w, y n, j n,( N j) ( x( j) + sin( θ )) sin( θ ) + ( y( j) cos( θ )) cos( θ ) ( x( j) + sin( θ )) + ( y( j) cos( θ )) ( x( j) + sin( θ )) cos( θ ) ( y( j) cos( θ )) sin( θ ) ( x( j) + sin( θ )) + ( y( j) cos( θ )) ( j) = cos ( j ϕ ½ ϕ) j = 1, y( j) = sin ( j ½ ) j = 1, ϕ dθ dθ ϕ 10 Danish Wind Power Research 013, May , HAa Madsen

11 Results Solidity σ = Bc R 11 Danish Wind Power Research 013, May , HAa Madsen

12 Results flow 1 Danish Wind Power Research 013, May , HAa Madsen

13 A modified linear AC model The same method of solution (linear and non-linear part) is used for the D actuator disc: v x v y p 1 y 1+ y = 1 arctg + arctg p π x x = p x + ln 4π x + y ( y + 1) ( 1) * CT = 4a lin However, from BEM theory we have: C T = 4a 4a To achieve a modified linear solution we multiply the 13 inductions with the factor k a 1 = 1 a Danish Wind Power Research 013, May , HAa Madsen

14 Results modified linear AC model 14 Danish Wind Power Research 013, May , HAa Madsen

15 Results modified linear AC model 15 Danish Wind Power Research 013, May , HAa Madsen

16 Results - 5MW DeepWind nd design Baseline design rotor radius 60.51m blade chord 5.0m rotor height 143.0m airfoil NACA0018 number of blades solidity 0.17 rated power rated speed swept area 5000kW 5.63rpm 1318m 16 Danish Wind Power Research 013, May , HAa Madsen

17 Results from baseline to nd design 17 Danish Wind Power Research 013, May , HAa Madsen

18 Results -5MW baseline DeepWind design 18 Danish Wind Power Research 013, May , HAa Madsen

19 Results -5MW baseline DeepWind design 19 Danish Wind Power Research 013, May , HAa Madsen

20 Conclusions The aeroelastic model HAWC 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 0 Danish Wind Power Research 013, May , HAa Madsen

21 Acknowledgement The DeepWind project is supported by the European Commission, Grant FP7 Energy 010- 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) 1 Danish Wind Power Research 013, May , HAa Madsen

22 Thank you for your attention Danish Wind Power Research 013, May , HAa Madsen