MAXIMUM LOADS ON A 1-DOF MODEL-SCALE OFFSHORE WIND TURBINE

Transcription

1 MAXIMUM LOADS ON A 1-DOF MODEL-SCALE OFFSHORE WIND TURBINE Loup Suja-Thauvin (Industry PhD) Jørgen Krokstad (prof II) Joakim Fürst Frimann-Dahl (DNV-GL)

2 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 2

3 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 3

4 1. Motivation Increasing rotor diameter

5 1. Motivation Focus on - Large diameter monopiles - Shallow waters increase of non-linearities (frequent breaking) ULS: what is the design driver?

6 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 6

7 2. Experiments Top mass 451 t Responding model Accelerometer Stiff section Pile diameter 6.9 m Water depth 2.9, 3m Force and moment transducer 7

8 2. Experiments Top view Parabolic beach Wave gauges Piston wavemaker Side view 8

9 2. Experiments Sea states: JONSWAP spectra Storms with different return periods 2 seeds per sea state H s (m) T p (s) g

10 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 1

11 3. Numerical model Representation of the model: 1 degree of freedom equation M hyyyy = I P + I A θ + Cθ + KK 1 Measured moment 5 Simulated moment Moment [Nm] Time [s]

12 3. Numerical model Input hydrodynamic loads from FNV formulation F FFF = 2πππ 2 u t z dd h + 2πππ 2 u t z= ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd h O ε O ε 2 +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 Finite water depth formulation

13 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 13

14 Focus on maximum responses - Very long and steep waves hit the structure - Frequent breaking waves - 1 st eigenperiod of the structure is excited

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18 FNV matches the maximum load 1 Hs = 9.4m, Tp = 11.25s, h = 3m FNV 5 Measured Moment [Nm] Time [s] 18

19 How does the 1 st mode get triggered? Measured wave spectrum 1st eigenfrequency t d = 13R 32c 5 Not much energy from the waves Frequency [Hz] 19

20 Input hydrodynamic loads from FNV formulation F FFF = 2πππ 2 u t z dd h + 2πππ 2 u t z= ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd h O ε O ε 2 +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 Contribution of linear potential at the free surface

21 Measured wave

22 Decomposition of the response into different modes 5 Excitation load Response without first mode Mf2Free 1st mode response 1 5 For all cases, there is a hump in the 2 nd order excitation load Mf2Free 1 2nd mode response (artificial second mode is triggered by slamming)

23 Simple approximation: trying to match the 2 nd order load with an impulse load of sinusoidal shape DLF max 1.5 M i Impulse load 1.5 -M t i t /T d d /2 t d

24 Simple approximation: trying to match the 2 nd order load with an impulse load of sinusoidal shape The free surface 2 nd order load has a high energy content around the eigenfrequency of the structure DLF max M i Impulse load -M t i t /T d d /2 t d

25 Decomposition of the response into different modes 5 Excitation load Response without first mode Mf2Free 1st mode response 1 5 Phase difference Mf2Free 2nd mode response

26 Analytical formula for the response 15 6 t M M ( t) = M cos( ωt) + sin( ωt) + ωm a f ( τ ) sin[ ω( t τ )] dτ ω with M the response moment of the structure M moment at initial state M a load amplitude f load shape function ω eigenperiod of the system Bending moment [Nm] -5-1 Mf2Free Impulse load 1st mode response -2-4 Bending moment [Nm] -15 Analytical response Time [s]

27 Analytical formula for the response 15 6 t M M ( t) = M cos( ωt) + sin( ωt) + ωm a f ( τ ) sin[ ω( t τ )] dτ ω Initial conditions are necessary to match the maximum value and phase Bending moment [Nm] Mf2Free Impulse load 1st mode response Analytical response Bending moment [Nm] Time [s]

28 Input hydrodynamic loads from FNV formulation F FFF = 2πππ 2 u t z dd h + 2πππ 2 u t z= ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd h O ε O ε 2 +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3

29 F FFF = 2πππ 2 h u t z dd + 2πππ 2 u t ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd z= h O ε 2 O ε +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 1 Mf2Free 5 Moment [Nm] Time [s]

30 F FFF = 2πππ 2 h u t z dd + 2πππ 2 u t ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd z= h O ε 2 O ε +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 1 Mf2Free Mf3Xsi 5 Moment [Nm] Time [s]

31 F FFF = 2πππ 2 h u t z dd + 2πππ 2 u t ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd z= h O ε 2 O ε +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 1 Mf2Free Mf3Xsi Mf31 5 Moment [Nm] Time [s]

32 Input hydrodynamic loads from FNV formulation F FFF = 2πππ 2 h u t z dd + 2πππ 2 u t ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd z= h O ε 2 O ε ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 DLF max M i Impulse load +ππ R2 g u2 u t β h z= R O ε 3 -M i t /2 t d d t /T d

33 F FFF = 2πππ 2 h u t z dd + 2πππ 2 u t ζ 1 + ππr 2 2w(z)w x (z) + u(z)u x (z) dd z= h O ε 2 O ε +ππr 2 ζ 1 u tt ζ 1 + 2ww x + uu x 2 g u tw t u t g u 2 + v 2 z= O ε 3 +ππ R2 g u2 u t β h z= R O ε 3 1 Mf2Free Mf3Xsi Mf31 5 Mf21 Moment [Nm] Time [s]

34 Damping considerations: - Low damping due to idling turbine (here 2.4%) - If the turbine is already oscillating, maximum load can be amplified or decreased depending on initial conditions

35 Table of contents 1. Motivation 2. Presentation of experiments 3. Numerical model 4. Analysis of the results 5. Conclusion 35

36 5. Conclusion Simple model to explain qualitatively maximum loads observed during experiments with high frequency of breaking waves Impulsive slamming has shown not to induce 1st mode shape response The maximum load can be explained as the transient response to an impulse load caused by higher order hydrodynamic loads components Low damping can potentially increase the maximum load by changing the initial conditions 2 nd mode of the structure is triggered by breaking and should be taken into consideration when assessing maximum loads

37 Acknowledgments The experiments were done using the set-up developed by Statoil for the Dudgeon project

38 TAKK