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Safety and Reliability

A New Numerical Tool for Fast Ships in Following Seas

[+] Author and Article Information
Ray-Qing Lin, John G. Hoyt

Department of Hydromechanics, Naval Surface Warfare Center Carderock Division (NSWCCD), West Bethesda, MD 20817-5700

J. Offshore Mech. Arct. Eng 132(3), 031602 (Jun 24, 2010) (10 pages) doi:10.1115/1.4000502 History: Received May 05, 2008; Revised July 27, 2009; Published June 24, 2010; Online June 24, 2010

The six-degrees-of-freedom ship motions of a ship at speeds other than zero are always measured in terms of encounter frequency, and often, the incident waves in experimental data are also measured only in the encounter frequency domain. Using these measured data to obtain transfer functions from irregular following sea ship motions is complicated by the combined effects of very low encounter frequencies and the “folding” of the sea spectra. This results in having both overtaking and encountered waves of the same encounter frequency but different wavelengths. Computing transfer functions becomes untenable when the ship speed approaches the wave phase velocity, where the encounter spectrum has a mathematical singularity.St. Denis and Pierson (1953, “On the Motions of Ships in Confused Seas,” Soc. Nav. Archit. Mar. Eng., Trans., 61, pp. 280–357) suggested the basic relationships between response ship motions or moments that can be developed in the wave frequency domain at the outset. The St. Denis–Pierson method is based on a linear theory and works well when the ship response regime is linear or weakly nonlinear. However, for high-speed craft operating at different headings where the problems are nonlinear, especially strongly nonlinear, the St. Denis–Pierson assumptions will break down inducing error (1953, “On the Motions of Ships in Confused Seas,” Soc. Nav. Archit. Mar. Eng., Trans., 61, pp. 280–357). Furthermore, using the frequency resolution method to remove the singularity point may also induce errors, especially when the singularity point is located near the peak of stationary frequency. How to obtain the correct frequency resolution in the local region of singularity point is still an unsolved problem. In this study, we will propose a new method capable of predicting ship response motions for crafts with nonlinear or strongly nonlinear behaviors quantitatively. For example, using this method, one can use measured ship motion data in head seas to predict the motions of the ship at high speed in following seas. The new method has six steps, including using a filter to eliminate those unexpected modes that are not from incident waves, inertial motions, or nonlinear interactions, and applying a higher-order Taylor expansion to eliminate the singularity point. We refer to the new method as the Lin–Hoyt method, which agrees reasonably well with computations of the nonlinear “digital, self-consistent, ship experimental laboratory ship motion model,” also known as DiSSEL (2006, “Numerical Modeling of Nonlinear Interactions Between Ships and Surface Gravity Waves II: Ship Boundary Condition,” J. Ship Res., 50(2), pp. 181–186). We also use experimental head sea data to validate the simulations of DiSSEL. The Lin–Hoyt method is fast and inexpensive. The differences in the results of the numerical simulations obtained by the Lin–Hoyt method and other linear methods diverge rapidly with increased forward ship speed due to the nonlinearity of ship motion responses.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) PSD; (b) PSD moving in head seas; (c) discrete spectrum of incident wave (sea state is 2.5); (d) phase angle distribution of incident wave

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Figure 2

(a) Comparison of heave motions for the PSD in the displacement mode; (b) comparison of pitch motions for the PSD in the displacement mode

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Figure 3

(a) Comparison of heave motions for the PSD in the planing mode; (b) comparison of pitch motions for the PSD in the planing mode

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Figure 4

(a) Comparison of the numerical prediction of heave motion for the PSD in the displacement mode in following seas; (b) comparison of the numerical prediction of pitch motion for the PSD in the displacement mode in following seas

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Figure 5

(a) Comparison of the numerical prediction of heave motion for the PSD in the planing mode in following seas; (b) comparison of the numerical prediction of pitch motion for the PSD in the planing mode in following seas

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Figure 6

(a) Encounter discrete R2 spectrum of numerical simulations of heave motion and incident waves in following seas, where R is the indicated variable; the amplitude of the incident wave, heave motion, pitch motion, etc. units for R are feet for incident waves, heave motion, and degrees for pitch motion; (b) encounter discrete R2 spectrum of numerical simulations of pitch motion and incident waves in following seas; units for R are feet for incident waves, and degrees for pitch motion

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Figure 7

(a) Encounter discrete R2 spectrum of incident waves, heave and pitch motions in head seas, units R are feet for incident waves and heave, and degrees for pitch motion; (b) discrete R2 spectrum transformed to the stationary R2 discrete spectrum using the transformation function in Eqs. 17,18,19; units R are feet for incident waves and heave, and degrees for pitch motion; (c) the encounter frequency in following seas varies with frequency

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Figure 8

(a) Filter method to eliminate the high frequencies noise from stationary discrete spectrum of the pitch motion; (b) encounter discrete R2 spectrum of pitch motion for the following seas; (c) the phase distribution of pitch motion for the PSD in the following seas; (d) comparison of the numerical simulation of the pitch motions between the DiSSEL simulation and the new method; (e) comparison of the numerical simulation of the heave motion between the DiSSEL simulation and the new method; (f) comparison of the numerical simulation of pitch motion between the DiSSEL model, the new method, and LAMP; (g) comparison of the numerical simulation of heave motion between the DiSSEL, the new method, and LAMP

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