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
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 7-8 013, HAa Madsen
Small on-shore Vertical Axis Wind Turbines Windpower tree Quiet revolution http://www.windpower tree.com/products.htm l http://windpowerdirectory.net/manufacturers/vaw t/quiet-revolution-s14.html http://windpowerdirectory.net/manu facturers/vawt/wepower-creatingand-delivering-clean-energysolutions-s41.html 3 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
HAWC developed from 003-006 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 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
How to compute the flow field for the AC model? 8 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
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,... 36 y( j) = sin ( j ½ ) j = 1,... 36 ϕ dθ dθ ϕ 10 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
Results Solidity σ = Bc R 11 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
Results flow 1 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
Results modified linear AC model 14 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
Results modified linear AC model 15 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
Results from baseline to nd design 17 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
Results -5MW baseline DeepWind design 18 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
Results -5MW baseline DeepWind design 19 Danish Wind Power Research 013, May 7-8 013, HAa Madsen
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 7-8 013, HAa Madsen
Acknowledgement The DeepWind project is supported by the European Commission, Grant 56769 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 7-8 013, HAa Madsen
Thank you for your attention Danish Wind Power Research 013, May 7-8 013, HAa Madsen