1. 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

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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.

17. Thanks for your attention
END

18. 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