EWEA Annual Event 2013 Vienna February, 4-7, 2013 Analysis of Vortex-induced Vibrations using a free-wake aeroelastic tool Spyros Voutsinas (*) Fangmao Zou(**), Vasilis Riziotis(*), Jun Wang(***) (*) NTUA, School of Mechanical Engineering, Greece (**) China-EU Institute for Clean and Renewable Energy, Wuhan, China (***) Huazhong University of Science and Technology, Wuhan, China

Vortex-induced vibrations & wind turbines Aeroelastic instabilities and vortex-induced vibrations can appear on wind turbine blades at stand still. Negative (CL-a) slope a~90o triggers Aeroelastic instabilities Large vortex structures trigger Vortex induced vibrations Du96-w-180: Skrzypiński et al, DTU 2012

Validation The double wake model Cdmax Clmin Clmax Cdmax v-, P+ v+, P- Clmax Cdmax v+, P- v-, P+ Finite: 𝑢 = 𝑢 𝜖 , 𝑟 2 → 𝑟 2 + 𝜖 2 Good agreement in the prediction of the lift slope, critical for aeroelastic damping characterization

about 10% shift in vortex shedding frequency Validation about 10% shift in vortex shedding frequency PSD of CL PSD of CD PSD of CL PSD of CD

Forced vibration results 𝑷 ∗ - 𝑻 ∗ curve of different A*/T* max 𝑃 ∗ appears at vibration periods 9.7 or 9.8 which are close to the vortex shedding period 10. Cl time series with different A*/T*, α=90° 𝒇 𝒗 =𝟎.𝟏 𝐇𝐳 𝑨 ∗ 𝑻 ∗ = 𝑨 𝑻𝑽 = 𝑨𝝎 𝟐𝝅𝑽 = 𝑼 𝒎𝒂𝒙 𝟐𝝅𝑽 = 𝟏 𝟐𝝅 ∙𝐭𝐚𝐧 𝜷 𝒎𝒂𝒙

Forced vibration results (d) T*=10 (e) T*=11 (f) T*=13 (a) 𝑻 ∗ =𝟕 (b) 𝑻 ∗ =𝟗 (c) 𝑻 ∗ =𝟗.𝟖 Cl-x plot of A*/T*=0.03 series

Aeroelastic simulations Typical blade section model V w u Structural model with 3 d.o.f. 𝜃 u: edgewise displacement w: flapwise displacement 𝜃: torsional angle k: spring coefficient 𝝃 𝒄𝒎 : the distance between the gravity center and the elastic axis V: inflow velocity

Aeroelastic simulations eigenvalue stability analysis flap mode high damping of flap mode driven by high CD value damping driving parameter edge mode damping of edge mode driven by negative slope of CL and CD value m=165 kg/m, fflap =0.7 hz, fedge =1.1 hz c=2.8 m (r/R=0.7), d=1.25% (=0.2%) wind speed 25 m/s

Aeroelastic simulations eigenvalue stability analysis: reference to “reality” 3D aerodynamic characteristics damping driving parameter edge mode m=165 kg/m, fflap =0.7 hz, fedge =1.1 hz c=2.8 m (r/R=0.7), d=1.25% (=0.2%) wind speed 25 m/s

Aeroelastic simulations eigenvalue stability analysis – effect of mass and chord length wind speed 25 m/s C=2.8 C=1.6

Aeroelastic simulations eigenvalue stability analysis – effect of structural properties wind speed 25 m/s Edge frequency structural pitch m=165 kg/m, c=2.8 m: (Rf=0.021) fflap =0.7 hz, fedge =1.1 hz

Aeroelastic simulations non-linear aeroelastic stability analysis Strongly non linear behaviour. Difficult to measure damping aoa = 90o 10s excitation period at the frequency of the edge mode (1.1 hz) wind speed 25 m/s m=165 kg/m, c=2.8 m (Rf=0.021) fflap =0.7 hz, fedge =1.1 hz

Aeroelastic simulations non-linear aeroelastic stability analysis aoa = 100o wind speed 25 m/s m=165 kg/m, c=2.8 m (Rf=0.021) fflap =0.7 hz, fedge =1.1 hz

Aeroelastic simulations analysis of lock-in due to vortex shedding fflap =0.7 hz, fedge =1.1 hz m=165 kg/m, c=2.8 m (Rf=0.021) U=10 m/s fs1=0.36hz fs2=0.71hz U=15 m/s fs1=0.54hz fs2=1.07hz U=20 m/s fs1=0.71hz fs2=1.43hz

Aeroelastic simulations analysis of lock-in due to vortex shedding fflap =0.7 hz, fedge =1.1 hz m=165 kg/m, c=2.8 m (Rf=0.021) U=25 m/s fs1=0.89hz fs2=1.79hz U=30 m/s fs1=1.07hz fs2=2.14hz fs1=1.25hz fs2=2.50hz U=35 m/s

Conclusions The double wake model has been successfully applied The cut-off length acts as calibration parameter. Good results were obtained for relatively large values Lock-in was detected at the shedding frequency corresponding to T~10. The positive feedback between the lock-in phenomenon and the structural vibration is found to be the main reason for the vortex induced aero-elastic instability.

Thanks for your attention END

Aeroelastic simulations analysis of lock-in due to vortex shedding fflap =0.7 hz, fedge =1.1 hz m=165 kg/m, c=2.8 m (Rf=0.021) flapwise deflection flap deflection edgewise deflection