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Research Papers: Ocean Engineering

The Nonlinear Roll Damping of a FPSO Hull

[+] Author and Article Information
Allan C. de Oliveira

PETROBRAS R&D Center,
CENPES,
21941-915 Rio de Janeiro, Brazil
e-mail: allan_carre@petrobras.com.br

Antonio Carlos Fernandes

LOC/COPPE – UFRJ,
PO BOX 68508,
21945-970 Rio de Janeiro, Brazil
e-mail: acfernandes@peno.coppe.ufrj

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 16, 2010; final manuscript received October 9, 2013; published online December 27, 2013. Assoc. Editor: Dominique Roddier.

J. Offshore Mech. Arct. Eng 136(1), 011106 (Dec 27, 2013) (10 pages) Paper No: OMAE-10-1023; doi: 10.1115/1.4025870 History: Received February 16, 2010; Revised October 09, 2013

The ship-rolling problem is a subject that has been studied for a long time. Since Froude's time (in the 19th century) to nowadays, this subject was revisited several times in order to adjust the theory to changes in ship hulls, dimensions, materials, appendages, etc. On the other hand, ship analysis technological resources, including both experimental techniques and computational capacity (that did not exist in Froude's time), have also amazingly improved. But despite all those technological developments, the assessment of the nonlinear roll damping of some types of hulls still is a challenging problem. The floating production storage and offloading (FPSO) hull fitted with larger bilge keels, for instance, has behaved in such a way that it is impossible to obtain results from nowadays industry standards via decaying tests. This paper discusses an alternative way to assess the nonlinear damping behavior of FPSO hulls with large bilge keels. Since it is fairly easy to perform decaying tests, the paper also proposes an alternative way to analyze the FPSO properties through this kind of testing by grouping multiple results instead of using only a single test. This artifice brought improvements, such as an increased agreement between the alternative model and the experimental data. The paper also compares the more traditional approaches with the alternative method and finally shows the latter's applicability.

Copyright © 2014 by ASME
Topics: Damping , FPSO , Hull , Keel , Ships , Modeling , Fittings
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References

Froude, W., 1861, “On the Rolling of Ships,” RINA Transactions and Annual Report 1861, London.
Froude, W., 1873, “On the Influence of Resistance Upon the Rolling of Ships,” Nav. Sci., 1, pp. 411–429; (http://www.gracesguide.co.uk/William_Froude)
Ikeda, Y., Himeno, Y., and Tanaka, N., 1978, “Components of Roll Damping of Ship at Forward Speed,” J. Jpn. Soc. Nav. Archit., 143, pp. 113–125; ISSN:0514-8499; (http://astp.jst.go.jp/modules/search/DocumentDetail/0514-8499_1978_143_Components%2Bof%2BRoll%2BDamping%2Bof%2BShip%2Bat%2BForward%2BSpeed_N%252FA) [CrossRef]
Himeno, Y., 1981, Prediction of Ship Roll Damping: A State of the Art, Michigan Univ., Ann Arbor. Dept. of Naval Architecture and Marine Technical Report (http://www.ntis.gov/search/product.aspx?ABBR=ADA112282)
Ikeda, Y., 2004, “Prediction Methods of Roll Damping of Ships and Their Application to Determine Optimum Stabilization Devices,” Marine Technol., 41(2), pp. 89–93.
Downie, M. J., Bearman, P. W., Graham, J. M. R., 1988, “Effect of Vortex Shedding on the Coupled Roll Response of Bodies in Waves,” J. Fluid Mech., 189, pp. 243–264. [CrossRef]
Yeung, R. W., and Cermelli, C., 1998, “Vortical Flow Generated by a Rolling Plate in a Free Surface,” in Free Surface Flows with Viscosity, ed. P. A.Tyvand, (Computational Mechanics Publisher): pp. 1–35, ISBN 978-1-85312-295-8 (http://en.wikipedia.org/wiki/Ronald_W._Yeung).
Oliveira, A. C., 2003, “Investigações sobre a Teoria Bilinear na Análise do Balanço Transversal de FPSOs (Investigation About the Bilinear Theory for the Analysis of FPSO Rolling),” M.Sc. thesis, COPPE/Federal University of Rio de Janeiro, Rio de Janeiro, Brazil (in Portuguese).
Aloisio, G., and Felice, F., 2006, “PIV Analysis Around the Bilge Keel of a Ship Model in a Free Roll Decay,” XIV Congresso Nazionale A. I. VE. LA., Rome, Italy, Nov. 6–7.
Jung, K. H., Chang, K., and Huang, E. T., 2005, “Two-Dimensional Flow Characteristics of Wave Interactions With a Free-Rolling Rectangular Structure,” Ocean Eng., 32, pp. 1–20. [CrossRef]
Wanderley, J. B. V., Ramiro, A., Reis, T., Fernandes, A. C., and Levi, C., 2007, “Numerical Simulation of Roll Damping of a FPSO,” XXVI International Symposium on Offshore Mechanics and Arctic Engineering (OMAE), San Diego, CA, June 10–15, Paper No. OMAE2007-29017.
Kinnas, S. A., 2004, “FPSO Roll Motions,” Texas A&M University Technical Report No. B157.
Yeung, R. W., and Ananthakrishnan, P., 1992, “Oscillation of a Floating Body,” J. Eng. Math., 26, pp. 211–230. [CrossRef]
Oliveira, A. C., and Fernandes, A. C., 2009, “New Ideas About an Old Subject: The Roll Damping Assessment via Model Testing,” Deepwater Offshore Specialty Symposium, Harbin, China, Jan. 16–19.
Fernandes, A. C., and Oliveira, A. C., 2009, “The Roll Damping Assessment via Decay Model Testing (New Ideas About an Old Subject),” J. Mar. Sci. Appl., 8(2), pp. 144–150. [CrossRef]
Faltinsen, O. M., 1990, Sea Loads on Ships and Offshore Structures, Cambridge University, Cambridge, UK.
Roberts, J. B., 1985, “Estimation of Non-Linear Ship Roll Damping From Free-Decay Data,” J. Ship Res., 29(2), pp. 127–138.
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Björck, A., 1996, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA.

Figures

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Fig. 1

Particle-induced visualization (PIV) velocity field at early stages of the decaying test (larger angles) shot at the instant when the cylinder is moving up; note that the vortex is affecting the hull pressure, but the first stronger vortex (position A) attracts the second vortex (position B) away from the hull (sling mode)

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Fig. 2

Particle-induced visualization (PIV) velocity field at later stages of the decaying test (smaller angles) at the time when the cylinder is moving up. Note that the vortex is barely affecting directly the hull pressure: it catches a small vortex 45 deg street being shed from the hull (fishtailing mode).

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Fig. 3

An example of multiple decay tests for a FPSO typical hull. The tests were performed for the model without bilge keel and with a large one. It can be noted how the bilge keel changes the behavior of the system, not only the magnitude but also the shape of the curve; each point is obtained by linear matching at each peak-to-peak cycle (the mean angle is the arithmetic average of these peak values).

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Fig. 4

Froude method applied to FPSO decay test extracted from Oliveira and Fernandes [14]. It can be observed an almost perfect match between simulation (continuous line) and experiment (dotted line). The coefficients are obtained by fitting a parabola to the experimental data; due to obvious reasoning, the origin is included in this fitting.

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Fig. 5

Faltinsen method applied to FPSO decay test extracted from Oliveira and Fernandes [14]. Again, an almost perfect match may be observed between test (dotted line) and simulation (continuous line).

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Fig. 6

Comparison between a decay test and a simulation considering bilinear modeling. The fitting procedure for the coefficients is described in Oliveira et al. [19]; the match is perfect within numerical errors.

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Fig. 7

Comparison among decay tests and simulations considering quadratic (Faltinsen and Froude) and bilinear modeling for the case of typical FPSO hull, with extended bilge keels; it can be noted the degradation of the quadratic solutions while the initial angle increases, mainly for Faltinsen modeling, the most used by the industry

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Fig. 8

Offsets of FPSO model used in tests

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Fig. 9

Quadratic analysis performed for several FPSO tests (considering the same model and different initial angles). The p1 coefficients increase with the initial angles shown in the Table 2.

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Fig. 10

Quadratic analysis performed for several FPSO tests (considering the same model and different initial angles). The p2 coefficients decrease with the initial angles shown in the Table 2.

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Fig. 11

Bilinear analysis performed for several FPSO tests (considering the same model and different initial angles); the large coefficient varies according to the initial angle until a limit, indicating a transition effect that is not accessed by the bilinear modeling

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Fig. 12

Several FPSO decay test data grouped together

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Fig. 13

FPSO decay test performed using the standard methodology (linear adjustment for a small-angle decay test) compared with grouped data

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Fig. 14

Traditional approach applied to the FPSO decay data set; as can be observed, the damping behavior is not well represented

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Fig. 15

Froude procedure (quadratic regression) applied to the FPSO decay data set; this kind of fitting seems better than the more used (Faltinsen) approach

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Fig. 16

Hyperbolical tangent behavior as a function of α parameter; as the parameter increases, the function better approximates to a step function

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Fig. 17

Least square nonlinear fitting using the Gauss–Newton algorithm for the data set plotted on Fig. 15 and the hyperbolical tangent–modified model

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Fig. 18

Damping behavior of the hyperbolic (based on the bilinear) model fitted by the Gauss–Newton algorithm for the data set of the FPSO with bilge keels and the conventional methodology

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Fig. 19

Comparison between decay test and simulation. The blue curve corresponds to a decay test used in the grouped coefficient estimation. The black curve is a numerical simulation considering the hyperbolic model adjusted to the grouped data; two situations were chosen: one with a large initial angle (a) and another with a very small initial angle (b).

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Fig. 20

FPSO mesh used as wamit® input to compute the parameters required for the regular wave analysis and comparison. The FPSO is the same used in the free decay tests.

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