Enhanced Unified Theory with Forward-Speed Effect Taken into Account in the Inner Free-Surface Condition

The enhanced unified theory (EUT) has been used as a core theory in the integrated system developed at the Research Initiative on Oceangoing Ships (RIOS) of Osaka University for predicting the propulsion and seakeeping performance of a ship in actual seas. In this study, the EUT is modified by adopting partially the solution method in the rational strip theory of Ogilvie and Tuck as a particular solution in the inner problem, thereby a forward-speed effect in the convection term of the free-surface condition is incorporated in the inner solution. This forward-speed effect is analytically shown to contribute only to the cross-coupling radiation forces. Some other forward-speed and 3D effects important in a low-frequency range are also included in the homogeneous component of the inner solution through matching with the outer solution in a similar manner to the unified theory of Newman. Numerical computations are implemented for a slender modified Wigley model and the RIOS bulk carrier model. Good agreement is confirmed in a comparison with experimental data for the cross-coupling added mass and damping coefficients between heave and pitch and also for the resulting ship motions, particularly in heave near the resonant frequency. The added resistance around the motion-resonant wavelength is found to be improved but sensitive to a slight change in heave and pitch motions. Thus, it is stressed that accurate prediction of the ship motions and resultant Kochin function is critical for more accurate prediction of the added resistance in waves.

An Investigation on Two-Dimensional Nonlinear Sloshing in Rectangular Tank

Two-dimensional liquid sloshing in rectangular tank of FLNG system is investigated both numerically and experimentally. In numerical simulation, a time-domain scheme has been developed based on potential flow theory in boundary element method. Tank movement is defined by wall boundary condition to produce a reciprocating oscillation. Nonlinear free surface condition is adopted to capture free surface elevation. Energy dissipation caused by viscous effects is considered by applying artificial damping term to the dynamic free surface condition, which is also vital to achieve a steady-state solution. For comparison, experiments of a rectangular tank filled with water subjected to specified oscillation are carried out. As coupling effects between sloshing and tank motion is not included in this research, the testing apparatus is required to produce consistent oscillation movement and not affected by the change of filling condition and sloshing load. Liquid surface elevations in several typical places of the tank were measured. Sloshing related parameters including oscillation amplitude, frequency and filling level are analyzed systematically. It’s found that numerical simulation results have good agreement with phenomenon observed under small amplitude excitation, and this nonlinear analysis method is proved to be effective in capturing liquid surface elevation. It is found that sloshing in tank is sensitive to filling level as well as excitation frequency, especially in the crucial combination cases of them. For given filling level, sloshing tends to be violent near corresponding natural frequencies, and viscous damping has limited contribution to sloshing amplitude when resonance occurs. This fundamental investigation also paves path for the study of more complicated sloshing problems.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.