Abstract:In this study, we conducted numerical simulations of fluid resonance in-between two floating structures based on potential theory assessing the effect of fluid viscosity by including the artificial damping force. The numerical results of two adjacent Barges systems and Barge & Wigley systems were compared with experimental data of those of the viscous fluid model based on Reynolds average Navier-Stokes equations (RANSE). It can be observed that the conventional potential flow model (without artificial damping force) significantly over-estimated the wave height and forces around the resonant frequencies. Results of the present method with an appropriate damping coefficient supported the available data, confirming the importance of the viscous damping effect on strong hydrodynamic interaction between the floating structures. Furthermore, influences of lateral clearances, wave heading angles, and ships' motions on the wave surface elevations were analyzed. Validation and application of methods to estimate the fluid resonant frequencies and modes were also conducted. Generally speaking, Molin's simplified theory can give an accurate estimation of resonant frequencies and serve as a practical tool to analyze the fluid resonant phenomena of gaps in-between a two Barge system and Wigley & Barge system in close proximity.

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Abstract:The singularities and oscillatory performance of translating-pulsating source Green's function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method (VSM), and steepest descent integration method (SDIM) were used to evaluate this type of Green's function. For SDIM, the complex domain was restricted only on the -plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating structures moving in waves.

The singularities, oscillatory performances and the contributing factors to the 3-D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.

A frequency domain analysis method based on the three-dimensional translating-pulsating (3DTP) source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to measure the wave loads and the free motions for a pair of side-byside arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating (3DP) source Green function. Numerical resonances and peak shift can be found in the 3DP predictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free surface and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two vessels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.