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Research Papers: Offshore Technology

Application of the Contour Line Method for Estimating Extreme Responses in the Mooring Lines of a Two-Body Floating Wave Energy Converter

[+] Author and Article Information
Made Jaya Muliawan

e-mail: made.muliawan@ntnu.no

Zhen Gao

e-mail: zhen.gao@ntnu.no

Torgeir Moan

e-mail: torgeir.moan@ntnu.no
Centre for Ship and Ocean Structures (CeSOS),
Norwegian University of
Science and Technology,
Otto Nielsens vei 10,
NO-7491, Trondheim, 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 April 3, 2012; final manuscript received March 29, 2013; published online June 6, 2013. Assoc. Editor: Lance Manuel.

J. Offshore Mech. Arct. Eng 135(3), 031301 (Jun 06, 2013) (10 pages) Paper No: OMAE-12-1033; doi: 10.1115/1.4024267 History: Received April 03, 2012; Revised March 29, 2013

The ultimate limit state (ULS) is one of the design criteria used in the oil and gas industry in mooring system design for floating platforms. The 100 year level response in the mooring line should be applied for the ULS design check, which is ideally estimated by taking into account the dynamic mooring line tension in all sea states available at the operational site. This approach is known as a full long-term response analysis using the all-sea-state approach. However, this approach is time consuming, and therefore, the contour line method is proposed for estimation of the 100 year response by primarily studying the short-term response for the most unfavorable sea states along the 100 year environmental contour line. Experience in the oil and gas industry confirmed that this method could yield good predictions if the responses at higher percentiles than the median are used. In this paper, the mooring system of a two-body wave energy converter (WEC) is considered. Because this system involves the interaction between two bodies, the estimation of the ULS level response using the all-sea-state approach may be even more time consuming. Therefore, application of the contour line method for this case will certainly be beneficial. However, its feasibility for application to a WEC case must be documented first. In the present paper, the ULS level response in the mooring tension predicted by the contour line method is compared to that estimated by taking into account all sea states. This prediction is achieved by performing coupled time domain mooring analyses using Simo/Riflex for six cases with different mooring configurations and connections between two bodies. An axisymmetric Wavebob-type WEC is chosen for investigation, and the Yeu site in France is assumed as the operational site. Hydrodynamic loads including second-order forces are determined using Wamit. Finally, the applicability of the contour line method for prediction of the ULS level mooring tension for a two-body WEC is assessed and shown to yield accurate results with the proper choice of percentile level for the extreme response.

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References

Det Norske Veritas (DNV), 2006, “Position Mooring,” Offshore Standard DNV-OS301.
NORSOK, 2007, “Actions and Action Effects,” NORSOK Standard N-003.
Winterstein, S. R., Ude, T. C., Cornell, C. A., Bjerager, P., and Haver, S., 1993, “Environmental Parameters for the Extreme Response: Inverse FORM With Omission Factors,” Proceedings of the ICOSSAR-1993, Innsbruck, Austria, pp. 551–557.
Haver, S., Sagli, G., and Gran, T. M., 1998, “Long Term Response Analysis of Fixed and Floating Structures,” Proceedings of the 1998 International OTRC Symposium, Houston, TX, pp. 240–248.
Wavebob, 2013, “Wavebob: Blue Energy,” Retrieved November 30, 2010, www.wavebob.com
Muliawan, M. J., Gao, Z., Moan, T., and Babarit, A., 2013, “Analysis of a Two-Body Floating Wave Energy Converter With the Particular Focus on the Effects of Power Take-Off and Mooring Systems on Energy Capture,” J. Offshore Mech. Arct. Eng. (accepted).
Mouwen, F., 2008, “Presentation on Wavebob to Engineers Ireland,” Retrieved September 10, 2010, www.engineersireland.ie
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Marintek, 2008, “SIMO User Manual—Program Version 3.6,” Marintek, Trondheim, Norway.
Babarit, A., Hals, J., Muliawan, M. J., Kurniawan, A., and Moan, T., 2012, “Numerical Benchmarking Study of a Selection of Wave Energy Converters,” Renewable Energy, 41, pp. 44–63. [CrossRef]
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WAMIT, Inc., 2006, “WAMIT User Manual—Program Version 6.3,” WAMIT, Chestnut Hill, MA.
Baarholm, G. S., and Haver, S., 2009, “Application of Environmental Contour Lines—The Summary of the Work so Far,” Proceedings of the International Conference on Floating Structures for Deepwater Operations, Glasgow, UK.
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Figures

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Fig. 4

One hundred year contour line for the wave conditions at the Yeu site

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Fig. 3

Mooring configurations considered in the simulations (only line 1 shown in the figure, symmetric for other lines)

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Fig. 2

(a) Location of the Yeu site specified as “A” (google map [9]) and (b) scatter diagram (presented in percentage) of waves at Yeu

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Fig. 1

(a) The wavebob concept [7] and (b) dimensions of the WEC used in the present analysis

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Fig. 5

Introduction of (a) mechanical coupling to allow the two bodies to move together in sway, surge, roll, and pitch yet move freely in heave and yaw; and (b) end stops to limit the relative heave motion

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Fig. 8

Tail parts of the long-term extreme response distributions obtained by the all-sea-state approach for the cases (a) with MC1 and (b) with MC4

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Fig. 6

Panel model for the present analysis

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Fig. 9

Illustration of the target percentile value that gives the same ULS tension as the all-sea-state approach result

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Fig. 10

Comparisons of 100 year mooring line tension resulting from the all-sea-state approach with those predicted using the contour line method with consideration of several percentile values for cases (a) MC1-LA, (b) MC1-L6, (c) MC1-UA, (d) MC4-LA, (e) MC4-L6, and (f) MC4-UA

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Fig. 11

Comparison of percentile level based on different numbers of samples: (a) samples and (b) fitted Gumbel distributions. The continous-connected dots in (a) and the solid fitted line in (b) are based on 400 samples (from Ref. [16]).

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Fig. 12

Differences between the responses obtained by the contour line method (XCL) considering several percentile levels and the 100-year response from the all-sea-state approach (XALL)

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Fig. 13

Heave RAOs of the WEC for different connections between two bodies

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