Numerical investigation on ship rolling responses coupled with nickel slurry flow inside tanks

In this paper, the rolling responses of a ship carrying nickel ore slurry are studied numerically to examine their dependences on water content of the slurry, incoming wave amplitude and the number of filling tanks. A combined non-Newtonian Herschel–Bulkley and Bingham model is used to describe the movement of the slurry inside the tanks. The proposed hybrid coupling model includes simulations of ship motion using impulse-response-function theory and internal sloshing using a viscous two-phase flow model based on OpenFOAM®. Benchmark scenarios for ship motion coupled with water sloshing in the tank are first examined. The responses reveal two peaks for the rolling amplitude over the incoming wave periods considered, one occurring before and the other occurring after the peak for ship motion without water sloshing in the tanks. In-phase and anti-phase relationships between ship-tank motion and the water free-surface inclination are identified at the two peaks of ship responses, respectively. For nickel slurries with a water content of less than 40% and an incoming wave amplitude of 0.025 m, the ship responses reveal only one peak over the wave periods examined. However, with the increase in water content or the increase in incoming wave amplitude, the ship responses also reveal the two-peak phenomena, indicating a transition for nickel slurries from a solid-like to a fluid-like state. The two-peak responses appear earlier at higher filling depths as wave amplitude or water content increases. This behavior indicates that nickel slurries exhibit greater stability (i.e., more solid-like behavior) at lower filling depths than that at higher ones. An increased number of filled tanks reduce the ship response at the resonant period, stabilizing the ship. Furthermore, loading the nickel slurries in more tanks raises the excitation threshold, requiring larger wave amplitudes for the slurry to transit from a solid-like to a fluid-like state.