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Research Papers: Ocean Renewable Energy

Fatigue Analysis of a Point Absorber Wave Energy Converter Subjected to Passive and Reactive Control

[+] Author and Article Information
A. S. Zurkinden

Department of Civil Engineering,
Aalborg University,
Aalborg 9000, Denmark
e-mail: azurkinden@gmail.com

S. H. Lambertsen

Department of Civil Engineering,
Aalborg University,
Aalborg 9000, Denmark

L. Damkilde

Professor
Department of Civil Engineering,
Aalborg University,
Aalborg 9000, Denmark

Z. Gao

Associate Professor
Centre for Ships and Ocean Structures,
Norwegian University of Science and Technology,
Trondheim 7031, Norway

T. Moan

Professor
Centre for Ships and Ocean Structures,
Norwegian University of Science and Technology,
Trondheim 7031, Norway

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received February 6, 2014; final manuscript received March 18, 2015; published online July 27, 2015. Assoc. Editor: António Falcão.

J. Offshore Mech. Arct. Eng 137(5), 051901 (Jul 27, 2015) (12 pages) Paper No: OMAE-14-1007; doi: 10.1115/1.4030646 History: Received February 06, 2014

This paper investigates the effect of a passive and reactive control mechanism on the accumulated fatigue damage of a wave energy converter (WEC). Interest is focused on four structural details of the Wavestar arm, which is used as a case study here. The fatigue model is set up as an independent and generic toolbox, which can be applied to any other global response model of a WEC device combined with a control system. The stress responses due to the stochastic wave loads are computed by a finite element method (FEM) model using the frequency-domain approach. The fatigue damage is calculated based on the spectral-based fatigue analysis in which the fatigue is described by the given spectral moments of the stress response. The question will be discussed, which control case is more favorable regarding the tradeoff between fatigue damage reduction and increased power production.

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References

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Zurkinden, A. , Kramer, M. , Sichani, M. , and Alves, M. , 2013, “Comparison Between Numerical Modeling and Experimental Testing of a Point Absorber WEC Using Linear Power Take-Off System,” ASME Paper No. OMAE2012-83692.
Zurkinden, A. , Ferri, F. , Beatty, S. , Kofoed, J. , and Kramer, M. , 2013, “Non-Linear Numerical Modeling and Experimental Testing of a Point Absorber Wave Energy Converter,” Ocean Eng., 78, pp. 11–21. [CrossRef]
Zurkinden, A. , Gao, Z. , Damkilde, L. , and Moan, T. , 2013, “Structural Modeling and Analysis of a Wave Energy Converter Applying Dynamical Substructuring Method,” ASME Paper No. OMAE2013-10854.
Zurkinden, A. , Gao, Z. , Lambertsen, S. , Damkilde, L. , and Moan, T. , 2013, “Fatigue Analysis of a Wave Energy Converter Taking Into Account Different Control Strategies,” ASME Paper No. OMAE2013-10864.
Hansen, R. , Kramer, M. , and Vidal, E. , 2013, “Discrete Displacement Hydraulic Power Take-Off System for the Wavestar Wave Energy Converter,” Energies, 6(8), pp. 4001–4044. [CrossRef]
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Zurkinden, A. , Sichani, M. , Gao, Z. , Damkilde, L. , and Moan, T. , “Nonlinear Motion Analysis of the Wavestar Wave Energy Converter With a Particular Focus on the Effect of Different Control Strategies on the Structural Response,” ASME Paper No. OMAE 2014-23796.
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Figures

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Fig. 1

Location of the Wavestar prototype device in Hanstholm Denmark. Left: northern Europe and right: picture of the prototype from the shoreline.

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Fig. 2

Left: WEC in operational mode. Right: WEC in protection mode.

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Fig. 3

Idealized Wavestar model, incident wave directions k=1..8:{0 deg:45 deg:360 deg}

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Fig. 4

Wave excitation moment for different incident wave angles. Left: real part of MFK,k+MD,k (Eq. (4)). Right: imaginary part.

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Fig. 5

Left: added mass a(ω) and damping coefficient b(ω). Right: nonlinear hydrostatic restoring moment MB in function of the pitch angle.

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Fig. 6

Wave directions and probability of occurrence, i.e., pk,1..8

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Fig. 7

Left: Plot of the average power function as a function of the control coefficient cc. Right: Surface plot of the power function as a function of the control coefficients cc and kc. The power functions are shown for a peak period of Tp=5.5 s and a unit wave amplitude.

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Fig. 8

Left: plot of the average power function as a function of the control coefficient cc. Right: surface plot of the power function as a function of the control coefficients cc and kc. The power functions are shown for a peak period of Tp=5.5 s and a unit wave amplitude.

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Fig. 9

SN curves in seawater with cathodic protection for F and W3 details according to Ref. [29]

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Fig. 10

Geometrical dimensions of the Wavestar arm and applied external loads

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Fig. 11

Structural details where the stress response analysis is carried out

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Fig. 12

Left: maxima of accelerations for strategy 1. Right: maxima of accelerations for strategy 2.

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Fig. 13

Left: maxima of control moment for strategy 1. Right: maxima of control moment for strategy 2.

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Fig. 14

Left: stress response spectrum for Hz=3.5 m Tz=5.0 s. Right: stress response spectrum for Hz=3.5 m Tz=6.0 s and incident wave angle of θ=0 deg. -: strategy 1 and -: strategy 2.

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Fig. 15

Maximum stress responses for a unit wave amplitude Hz=2.0 m as a function of the peak periods and wave directions. Left: strategy 1. Right: strategy 2 for Connection 3.

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Fig. 16

Accumulated fatigue damage for a unit wave amplitude Hz=2.0 m as a function of the peak periods and wave directions. Left: strategy 1. Right: strategy 2 for Connection 3.

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Fig. 17

Accumulated fatigue damage for a unit wave amplitude Hz=2.0 m as a function of the peak periods and wave directions. Left: strategy 1. Right: strategy 2 for Connection 4.

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