Coupling of Sloshing and Ship Motions

The coupled effect between ship motions and sloshing is studied. Two-dimensional experiments of a hull section containing tanks filled with different levels of water excited in sway by regular waves have been conducted. Steady-state results are obtained for the sway amplitude. Even if violent sloshing occurs in the tanks, the steady-state motion is almost linear and sinusoidal with the frequency of the linear incident waves. This implies that higher-order harmonics of the sloshing force are filtered out by the system. Simulations of the modeled case are performed using a linear and a nonlinear sloshing model and mainly assuming linear external flow. For steady-state motion, a convolution formulation does not improve the results relative to using constant coefficients in the equation of motion. However, in order to properly model the transient behavior in an irregular sea, a convolution formulation must be included. The treatment of the retardation function for the external problem is discussed in detail. A good agreement between experiments and computations is reported. The calculated coupled motion is sensitive to the damping of the sloshing motion in a certain frequency range where the coupled sloshing and ship motions cause resonant ship motions. A quasilinear frequency domain analysis is used to explain this by introducing the sloshing loads as a frequency dependent spring.