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

EWEA Annual Event 2013Vienna

February, 4-7, 2013

Vortex induced vibrations 2/16

Vortex-induced vibrations & wind turbines

Aeroelastic instabilities and vortex-induced vibrations can appear on wind turbine blades at stand still.

1. Negative (CL-a) slope a~90o triggers Aeroelastic instabilities

2. Large vortex structures trigger Vortex induced vibrations

Du96-w-180: Skrzypiński et al, DTU 2012


Validation

0.2 m

Good agreement in the prediction of the lift slope, critical for aeroelastic damping characterization

Finite:

The double wake model

Clmax Cdmax

v+, P-

v-, P+

ClminCdmax

v-, P+

v+, P-


PSD of CL PSD of CD

0.05 m

0.20 m

0.115 hzf =0.23 hzf =

0.10 hzf = 0.20 hzf =

about 10% shift in vortex shedding frequencyf

PSD of CL PSD of CD

Validation


Forced vibration results

max appears at vibration periods 9.7 or 9.8 which are close to the

vortex shedding period 10.

𝑨∗

𝑻 ∗= 𝑨𝑻𝑽 = 𝑨𝝎

𝟐𝝅𝑽 =𝑼𝒎𝒂𝒙

𝟐𝝅𝑽 = 𝟏𝟐𝝅 ∙ 𝐭𝐚𝐧 𝜷𝒎𝒂𝒙

Cl time series with different A*/T*, α=90

- curve of different A*/T*

𝒇 𝒗=𝟎 .𝟏𝐇𝐳


(d) T*=10 (e) T*=11 (f) T*=13

(a) (b) (c)

Cl-x plot of A*/T*=0.03 series

Forced vibration results


V

w

u

Structural model with 3 d.o.f.

𝜃

u: edgewise displacement

w: flapwise displacement𝜃: torsional angle

k: spring coefficient

: the distance between

the gravity center and the

elastic axis

V: inflow velocity

Aeroelastic simulations

Typical blade section model


angle of attack [deg]

dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 1300

1

2

3

4

5


dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 13040

50

60

70

80

Aeroelastic simulationseigenvalue stability analysis

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%)

high damping of flap mode driven by high CD value

flap mode

edge mode

damping of edge mode driven by negative slope of

CL and CD value

wind speed 25 m/s

LDdCCd

damping driving parameter



dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 130-6

-4

-2

0

2

4

6 2D CD (CDmax=2.0)3D CD (CDmax=1.3)

Aeroelastic simulationseigenvalue stability analysis: reference to “reality”

3D aerodynamic characteristics

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%)

edge mode

wind speed 25 m/s

LDdCCd

damping driving parameter

DmaxC 1.3



eigenvalue stability analysis – effect of mass and chord length


dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 1300

1

2

3

4

5

6

7

8 Rf=0.021Rf=0.042Rf=0.024

fR c / m= wind speed 25 m/s


dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 130-8

-6

-4

-2

0Rf=0.021 (CDmax=1.3)Rf=0.024 (CDmax=1.3)

C=2.8C=1.6



eigenvalue stability analysis – effect of structural properties

m=165 kg/m, c=2.8 m: (Rf=0.021)

wind speed 25 m/s


dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 130-8

-6

-4

-2

0 fedge=1.1hzfedge=0.9 hzfedge=0.8 hz


dam

ping

inlo

gde

crem

ent[

%]

50 60 70 80 90 100 110 120 130-8

-6

-4

-2

0

2

4 0 deg5 deg10 deg-5 deg-10 deg

structural pitchEdge frequency

fflap =0.7 hz, fedge =1.1 hz


Aeroelastic simulationsnon-linear aeroelastic stability analysis

time [s]

edge

wis

ede

flect

ion

[m]

50 100 150

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

m=165 kg/m, c=2.8 m (Rf=0.021)

wind speed 25 m/s


10s excitation period at the frequency of the edge mode (1.1

hz)

Strongly non linear behaviour. Difficult to measure damping aoa = 90o


liftc

oeffi

cien

tCL

40 60 80 100 120 140-1

-0.5

0

0.5

1unsteadysteady-state (mean CL)


Aeroelastic simulationsnon-linear aeroelastic stability analysis

m=165 kg/m, c=2.8 m (Rf=0.021)

wind speed 25 m/s


time [s]

ed

gew

ise

deflectio

n[m

]

20 30 40 50

-4

-2

0

2

4 aoa = 100o


liftc

oeffi

cien

tCL

40 60 80 100 120 140

-1

0

1

2unsteadysteady-state (mean CL)


time [s]

flapw

ise

defle

ctio

n[m

]

40 50 60 70 80 90 100-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

time [s]

edge

wis

ede

flect

ion

[m]

40 50 60 70 80 90 100-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

time [s]

flapw

ise

defle

ctio

n[m

]

40 50 60 70 80 90 100-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

time [s]

edge

wis

ede

flect

ion

[m]

40 50 60 70 80 90 100-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Aeroelastic simulationsanalysis of lock-in due to vortex shedding

time [s]

flapw

ise

defle

ctio

n[m

]

40 50 60 70 80 90 100-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

time [s]

edge

wis

ede

flect

ion

[m]

40 50 60 70 80 90 100-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

m=165 kg/m, c=2.8 m (Rf=0.021)


U=10 m/s

U=15 m/s

U=20 m/s

fs1=0.36hz fs2=0.71hz

fs1=0.54hz fs2=1.07hz

fs1=0.71hz fs2=1.43hz


time [s]

edge

wis

ede

flect

ion

[m]

40 50 60 70 80 90 100-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2


m=165 kg/m, c=2.8 m (Rf=0.021)


time [s]

flapw

ise

defle

ctio

n[m

]

40 50 60 70 80 90 100-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

time [s]

flapw

ise

defle

ctio

n[m

]

20 30 40 50 60 70 80-2

-1

0

1

2

3

4

5

time [s]ed

gew

ise

defle

ctio

n[m

]

20 30 40 50 60 70 80-10-8-6-4-202468

10

time [s]

flapw

ise

defle

ctio

n[m

]

20 30 40 50 60 70-3

-2

-1

0

1

2

3

4

5

6

time [s]

edge

wis

ede

flect

ion

[m]

20 30 40 50 60 70 80

-10

-5

0

5

10

U=25 m/s

U=30 m/s

U=35 m/s

fs1=0.89hz fs2=1.79hz

fs1=1.07hz fs2=2.14hz

fs1=1.25hz fs2=2.50hz


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



m=165 kg/m, c=2.8 m (Rf=0.021)


flapwise deflection

flap deflection

edgewise deflection

ewea annual event 2013 vienna february, 4-7, 2013

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