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Journal of Offshore Mechanics and Arctic Engineering | Volume 137 | Issue 5 | research-article
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
Article
References
Figures
Tables

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.
Copyright © 2015 by ASME
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References

1
Kramer, M. , Marquis, L. , and Frigaard, P. , 2011, “Performance Evaluation of the Wavestar Prototype,” 9th European Wave and Tidal Energy Conference (EWTEC), pp. 1–9.
2
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.
3
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]
4
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.
5
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.
6
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]
7
Hansen, R. , and Kramer, M. , 2011, “Modelling and Control of the Wavestar Prototype,” 9th European Wave and Tidal Energy Conference (EWTEC).
8
Nielsen, S. , Zhou, Q. , Kramer, M. , Biswajit, B. , and Zhang, Z. , 2013, “Optimal Control of Nonlinear Wave Energy Point Converters,” Ocean Eng., 72, pp. 176–187. [CrossRef]
9
Margheritini, L. , 2011, “Review on Available Information on Waves in the DanWEC Area,” Danwec Vaekstforum 2011, DCE Technical Report, Report No. 135.
10
Jiao, G. , and Moan, T. , 1990, “Probabilistic Analysis of Fatigue Due to Gaussian Load Processes,” Probab. Eng. Mech., 5(2), pp. 76–83. [CrossRef]
11
Gao, Z. , and Moan, T. , 2008, “Frequency-Domain Fatigue Analysis of Wide-Band Stationary Gaussian Processes Using a Trimodal Spectral Formulation,” Int. J. Fatigue, 30(10–11), pp. 1944–1955. [CrossRef]
12
Dirlik, T. , 1985, “Application of Computers in Fatigue Analysis,” Ph.D. thesis, University of Warwick, Warwick, UK.
13
Benasciutti, D. , and Tovo, R. , 2007, “On Fatigue Damage Assessment in Bimodal Random Processes,” Int. J. Fatigue, 29(2), pp. 232–244. [CrossRef]
14
Nielsen, U. , Jensen, J. , Pedersen, P. , and Ito, Y. , 2011, “Onboard Monitoring of Fatigue Damage Rates in the Hull Girder,” Mar. Struct., 24(2), pp. 182–206. [CrossRef]
15
DET NORSKE VERITAS (DNV), 2012, “Fatigue Methodology of Offshore Ships,” Report No. DNV-RP-C206.
16
American Bureau of Shipping (ABS), 2005, Spectral-Based Fatigue Analysis for Floating Offshore Structures, ABS, Houston, TX.
17
Newman, J. , 1976, Marine Hydrodynamics, MIT Press, Cambridge, MA.
18
ANSYS, Inc., 2011, AQWA-LINE Manual, ANSYS, Canonsburg, PA.
19
Faltinsen, O. , 1990, Sea Loads on Ships and Offshore Structures, Cambridge University, Cambridge, UK.
20
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.
21
Guerinel, M. , Zurkinden, A. , Alves, M. , and Sarmento, A. , 2013, “Validation of a Partially Nonlinear Time Domain Model Using Instantaneous Froude–Krylov and Hydrostatic Force,” 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark, Vol. 10.
22
Sichani, M. , Chen, J. , Li, J. , Kramer, M. , and Nielsen, S. , 2013, “Constrained Optimal Stochastic Control of Non-Linear Wave Energy Point Absorber,” Appl. Ocean Res., 47, pp. 255–269. [CrossRef]
23
Taghipour, R. , Perez, T. , and Moan, T. , 2008, “Hybrid Frequency-Domain Models for Dynamic Response Analysis of Marine Structures,” Ocean Eng., 35, pp. 685–705. [CrossRef]
24
Yu, Z. , and Falnes, J. , 1975, “State-Space Modeling of a Vertical Cylinder in Heave,” Appl. Ocean Res., 17, pp. 265–275. [CrossRef]
25
DanWEC, http://www.danwec.com/
26
Det Norske Veritas (DNV), 2007, “Environmental Conditions and Environmental Loads,” Report No. DNV-RP-C205.
27
Gao, Z. , and Moan, T. , 2009, “Accuracy of the Narrow-Band Approximation of Stationary Wide-Band Gaussian Processes for Extreme Value and Fatigue Analysis,” 10th International Conference on Structural Safety and Reliability (ICOSSAR), pp. 997–1004.
28
Rice, S. , 1945, “Mathematical Analysis of Random Noise,” Bell Syst. Tech. J., 24(1), pp. 46–156. [CrossRef]
29
Det Norske Veritas (DNV), 2010, “Fatigue Design of Offshore Steel Structures,” Report No. DNV-RP-C203.
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ANSYS, Inc., 2011, ANSYS Manual Version 14.0.3, ANSYS, Canonsburg, PA.

Figures

Grahic Jump Location
Fig. 1

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

+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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Location of the Wavestar prototype device in Hanstholm Denmark. Left: northern Europe and right: picture of the prototype from the shoreline.
Grahic Jump Location
Fig. 2

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

+Left: WEC in operational mode. Right: WEC in protection mode.
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Left: WEC in operational mode. Right: WEC in protection mode.
Grahic Jump Location
Fig. 3

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

+Idealized Wavestar model, incident wave directions k=1..8:{0 deg:45 deg:360 deg}
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Idealized Wavestar model, incident wave directions k=1..8:{0 deg:45 deg:360 deg}
Grahic Jump Location
Fig. 4

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

+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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Wave excitation moment for different incident wave angles. Left: real part of MFK,k+MD,k (Eq. (4)). Right: imaginary part.
Grahic Jump Location
Fig. 5

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

+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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Left: added mass a(ω) and damping coefficient b(ω). Right: nonlinear hydrostatic restoring moment MB in function of the pitch angle.
Grahic Jump Location
Fig. 6

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

+Wave directions and probability of occurrence, i.e., pk,1..8
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Wave directions and probability of occurrence, i.e., pk,1..8
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
Fig. 9

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

+SN curves in seawater with cathodic protection for F and W3 details according to Ref. [29]
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SN curves in seawater with cathodic protection for F and W3 details according to Ref. [29]
Grahic Jump Location
Fig. 10

Geometrical dimensions of the Wavestar arm and applied external loads

+Geometrical dimensions of the Wavestar arm and applied external loads
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Geometrical dimensions of the Wavestar arm and applied external loads
Grahic Jump Location
Fig. 11

Structural details where the stress response analysis is carried out

+Structural details where the stress response analysis is carried out
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Structural details where the stress response analysis is carried out
Grahic Jump Location
Fig. 12

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

+Left: maxima of accelerations for strategy 1. Right: maxima of accelerations for strategy 2.
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Left: maxima of accelerations for strategy 1. Right: maxima of accelerations for strategy 2.
Grahic Jump Location
Fig. 13

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

+Left: maxima of control moment for strategy 1. Right: maxima of control moment for strategy 2.
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Left: maxima of control moment for strategy 1. Right: maxima of control moment for strategy 2.
Grahic Jump Location
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.

+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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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.
Grahic Jump Location
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.

+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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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.
Grahic Jump Location
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.

+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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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.
Grahic Jump Location
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.

+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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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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