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Research Papers: Ocean Engineering

Suppression of Irregular Frequency Effect in Hydrodynamic Problems and Free-Surface Singularity Treatment

[+] Author and Article Information
Yujie Liu

Marine Dynamics Laboratory,
Department of Ocean Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: yjliu2012@tamu.edu

Jeffrey M. Falzarano

Marine Dynamics Laboratory,
Department of Ocean Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: jfalzarano@civil.tamu.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 9, 2016; final manuscript received May 26, 2017; published online July 6, 2017. Assoc. Editor: Lance Manuel.

J. Offshore Mech. Arct. Eng 139(5), 051101 (Jul 06, 2017) (16 pages) Paper No: OMAE-16-1113; doi: 10.1115/1.4036950 History: Received September 09, 2016; Revised May 26, 2017

Multibody operations are routinely performed in offshore activities, for example, the floating liquefied natural gas (FLNG) and liquefied natural gas carrier (LNGC) side-by-side offloading case. To understand the phenomenon occurring inside the gap is of growing interest to the offshore industry. One important issue is the existence of the irregular frequency effect. The effect can be confused with the physical resonance. Thus, it needs to be removed. An extensive survey of the previous approaches to the irregular frequency problem has been undertaken. The matrix formulated in the boundary integral equations will become nearly singular for some frequencies. The existence of numerical round-off errors will make the matrix still solvable by a direct solver, however, it will result in unreasonably large values in some aspects of the solution, namely, the irregular frequency effect. The removal of the irregular effect is important especially for multibody hydrodynamic analysis in identifying the physical resonances caused by the configuration of floaters. This paper will mainly discuss the lid method on the internal free surface. To reach a higher accuracy, the singularity resulting from the Green function needs special care. Each term in the wave Green function will be evaluated using the corresponding analysis methods. Specifically, an analytical integral method is proposed to treat the log singularity. Finally, results with and without irregular frequency removal will be shown to demonstrate the effectiveness of our proposed method.

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Figures

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Coordinate setting

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Fig. 2

Coordinate setting for log singularity

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Shape of R0−ln(d−v) for 2 × 2 panel

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Shape of R0−ln(d−v) for 5 × 5 panel

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Shape of R0−ln(d−v) for 10 × 10 panel

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Shape of R0−ln(d−v) for 20 × 20 panel

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Fig. 7

Added mass A15 versus frequency ωL/g

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Added mass A33 versus frequency ωL/g

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Added mass A55 versus frequency ωL/g

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Fig. 10

Damping B11 versus frequency ωL/g

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Fig. 11

Damping B33 versus frequency ωL/g

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Damping B55 versus frequency ωL/g

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Surge drift force versus frequency ωL/g

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Pitch drift force versus frequency ωL/g

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Perspective view of miniboxbarge

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Added mass A51 versus frequency ωL/g

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Added mass A75 versus frequency ωL/g

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Added mass A11-7 versus frequency ωL/g

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Damping B57 versus frequency ωL/g

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Damping B33 versus frequency ωL/g

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Damping B55 versus frequency ωL/g

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Perspective view of two miniboxbarges (separation 10 m)

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Added mass A11 versus frequency ωL/g

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Added mass A15 versus frequency ωL/g

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Added mass A33 versus frequency ωL/g

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Added mass A55 versus frequency ωL/g

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Fig. 27

Perspective view of boxbarge

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Added mass A11 versus frequency ωL/g

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Added mass A15 versus frequency ωL/g

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Added mass A22 versus frequency ωL/g

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Added mass A24 versus frequency ωL/g

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Perspective view of cylinder dock

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Added mass A11 versus frequency ωL/g

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Added mass A51 versus frequency ωL/g

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Damping B11 versus frequency ωL/g

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Damping B15 versus frequency ωL/g

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Perspective view of BOB hope

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Added mass A11 versus frequency ωL/g

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Added mass A13 versus frequency ωL/g

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Added mass A33 versus frequency ωL/g

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Added mass A55 versus frequency ωL/g

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Fig. 42

Heave drift force versus frequency ωL/g

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Pitch drift force versus frequency ωL/g

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Fig. 44

Perspective view of BOBO

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Added mass A11 versus frequency ωL/g

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Fig. 46

Added mass A33 versus frequency ωL/g

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Added mass A55 versus frequency ωL/g

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Damping B11 versus frequency ωL/g

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Sway FKD force versus frequency ωL/g

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Fig. 50

Pitch FKD force versus frequency ωL/g

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Fig. 51

Perspective view of BOB hope–BOBO (separation 3 m)

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