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Research Papers: Offshore Technology

A Continuous Desingularized Source Distribution Method Describing Wave–Body Interactions of a Large Amplitude Oscillatory Body

[+] Author and Article Information
Aichun Feng

Department of Civil
and Environmental Engineering,
National University of Singapore,
Singapore 117576;
Faulty of Engineering and the Environment,
University of Southampton,
Southampton SO17 1BJ, UK

Zhi-Min Chen

School of Mathematics
and Computational Science,
Shenzhen University,
Shenzhen 518052, China;
Faulty of Engineering
and the Environment,
University of Southampton,
Southampton SO17 1BJ, UK
e-mail: zhimin@soton.ac.uk

W. G. Price

Faulty of Engineering and the Environment,
University of Southampton,
Southampton SO17 1BJ, UK;
WUT-UoS High Performance Ship Technology Joint Centre,
Wuhan 430063, China

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 January 6, 2014; final manuscript received January 13, 2015; published online February 6, 2015. Assoc. Editor: M. H. (Moo-Hyun) Kim.

J. Offshore Mech. Arct. Eng 137(2), 021302 (Apr 01, 2015) (10 pages) Paper No: OMAE-14-1001; doi: 10.1115/1.4029634 History: Received January 06, 2014; Revised January 13, 2015; Online February 06, 2015

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave–body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements.

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References

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Figures

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Fig. 1

Profile of the wave–body interaction problem caused by a body oscillating vertically

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Fig. 2

2D numerical model sketch

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Fig. 3

Heaving motion profile of sources, nodes, and intersection points at different time steps

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Fig. 4

Comparisons of the analytical solution given by Eq. (21) and numerical results for different panel numbers Nb

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Fig. 5

The variation of the error coefficients with panel numbers Nb (or Nb2)

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Fig. 6

Comparison of heave added mass coefficient between the experimental data of Vugts [18] and prediction adopting different free surface node point value Nf. The circular cylinder of beam B ( = 2 R) oscillates vertically with amplitude a = 0.1 T at a nondimensional frequency ωB/(2g).

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Fig. 7

Comparison of heave damping coefficient between the experimental data of Vugts [18] and prediction adopting different free surface node point value Nf. The circular cylinder of beam B ( = 2 R) oscillates vertically with amplitude a = 0.1 T at a nondimensional frequency ωB/(2g).

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Fig. 8

Comparison of node points distributions in the first four wave lengths between the proposed approach and Zhang and Beck's method [12,19]

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Fig. 9

Comparison of heave added mass coefficient A33 between Lee [23] numerical results, Yamashita [21] experimental data and current method prediction for a circular cylinder in oscillatory heave motion with amplitude a = 0.2 T

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Fig. 10

Comparison of heave damping coefficient B33 between Lee [23] numerical results, Yamashita [21] experimental data and current method prediction for a circular cylinder in oscillatory heave motion with amplitude a = 0.2 T

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Fig. 11

Comparisons of first order force F1(ω) between Zhang and beck [19] numerical results, Kent [22] numerical results, Tasai [24] experimental data and current method predictions for a circular cylinder in oscillatory heave motion with amplitude a = 0.2 T

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Fig. 12

Comparisons of first order force F2(ω) between Zhang and Beck [19] numerical results, Potash [25] numerical results, Parissis [26] numerical results, Yamashita [21] experimental data and current method predictions for a circular cylinder in oscillatory heave motion with amplitude a = 0.2 T

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Fig. 13

Comparisons of heave added mass coefficient A33 between Tasai [24] numerical results, Yamashita [21] experimental data and current method predictions for a wedge of the beam-to-draft ratio B/T=23/3 experiencing an oscillatory heave motion of amplitude a = 0.2 T

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Fig. 14

Comparisons of heave damping coefficient B33 between Tasai [24] numerical results, Yamashita [21] experimental data and current method predictions for a wedge of beam-to-draft ratio B/T=23/3 experiencing an oscillatory heave motion of amplitude a = 0.2 T

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Fig. 15

Predicted wave elevation time records at various amplitudes of heave oscillatory motion when ω2B/(2g)=1.0

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Fig. 16

Predicted vertical force time records at various amplitudes of heave oscillatory motion when ω2B/(2g)=1.0

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Fig. 17

Predicted pressure distributions around the circular cylinder at different times for heave amplitude a = 0.2 T and nondimensional frequency ωB/(2g)=1.0

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Fig. 18

Predicted pressure distributions around the oscillatory wedge of beam-to-draft ratio B/T=23/3 at different times for heave amplitude a = 0.2 T and nondimensional frequency ωB/(2g)=1.0

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Fig. 19

Comparisons of sway added mass coefficient A22 between Zhang [27] numerical results, Vugts [18] numerical results, Vugts [18] experimental data and current method predictions for a circular cylinder in oscillatory sway motion with amplitude a = 0.1 T

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Fig. 20

Comparisons of sway damping coefficient B22 between Zhang [27] numerical results, Vugts [18] numerical results, Vugts [18] experimental data and current method predictions for a circular cylinder in oscillatory sway motion with amplitude a = 0.1 T

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