Investigation into ship roll hydrodynamic coefficients using motion simulations

Dynamic stability is the field of naval architecture, which analyses the stability of a ship and the onset of instability in encountering waves at sea. The study of dynamic stability aims to investigate the development of extreme roll motion and to find out if a ship is stable or unstable. This understanding leads to broad implications for the design and operation of ships and floating units. Researchers have an integrated notion of “ship stability, dynamics and safety” for investigating dynamic stability phenomena. In practice, the intact stability for design and operation is evaluated through static conditions considering very basic and simplified condition, which does not account for the effects of real waves and winds at sea. This long-standing issue has been addressed by the second generation of intact stability criteria (SGISC) proposed by IMO in recent years, which defines a set of failure modes associated with potentially dangerous dynamic stability phenomena in waves. These phenomena are declared as parametric roll, pure loss of stability, surf-riding and broaching, dead ship condition and excessive acceleration. Among those, roll resonance occurs because of two different phenomena of synchronous and parametric roll, where the encounter frequency is equal and two times the ship’s natural roll frequency, respectively. The parametric roll is most probable to arise in some types of ships like containerships in a head sea condition when the wavelength is approximately equal to the ship’s length. Whereas, all ship types may be subjected to the synchronous rolling in beam sea conditions. The roll resonance is a dangerous dynamic condition where a ship experiences an incremental roll angle, and in the worst scenario a large roll angle may capsize the ship. At the roll resonance condition, the magnitude of virtual roll moment of inertia is equal to the restoring moment but in the opposite direction, hence, they oppose each other and leave roll damping to resist the roll motion. Since the magnitude of roll damping is small for a typical ship, the external forces and moments induce a larger roll motion. The investigation of parametric roll and dead ship condition using experiments and CFD simulations are expensive in terms of cost and time, whereas equation-based methods (solving of mathematical models) with a reasonable level of accuracy can be more effective in terms of expenses. The mathematical models consist of the virtual roll moment of inertia (roll mass moment of inertia and roll added mass moment of inertia), damping and restoring moment coefficients. Therefore, this research aims to quantify those coefficients and their variations in different conditions. This study increases our understanding of the ship’s dynamic stability by precisely calculating the roll hydrodynamic coefficients in calm water and regular beam sea conditions. A numerical method is adopted and validated against experimental model tests to investigate the influence of several parameters on the magnitude of roll hydrodynamic coefficients in calm water condition including degrees of freedom (DOF), Froude number, excitation frequency, scale effect and appendages. In the second phase of the study, numerical and experimental simulations are conducted in regular beam sea conditions and a good correlation is found between the results. Furthermore, the effects of different wave heights and frequencies on the roll hydrodynamic coefficients in a beam sea condition are investigated. This study introduces new methods of calculating the roll hydrodynamic coefficients including roll added mass moment of inertia, damping and restoring in calm water and regular beam sea conditions. These methods can be generalised for application on other ship types to extract hydrodynamic coefficients applicable to equation-based methods for the precise prediction of ship motions. The findings are extremely useful for ship designers and researchers, which contribute in several ways to the understanding of ship stability and provide a basis for considering dynamic behaviours in the actual operational conditions