For a ship undergoing roll motion at a resonance frequency, the roll restoring moment and virtual moment of inertia counteract each other and only the damping moment resists the roll exciting moments. Hence, accurate computation of the roll damping moment improves the roll motion prediction. There are several methods to calculate the damping moment; however, most of them fail to consider the viscous effects, such as the potential theory-based method. The experimental measurements take into account the viscous effect; however, they are expensive. The Computational Fluid Dynamics (CFD) method is an alternative to accurately consider the viscous effect. In this study, a CFD approach based on harmonic exciting roll motion technique is adopted to compute the roll motion characteristics and damping coefficients at different conditions. The impact of appendages, Froude number, and degrees of freedom on roll motion characteristics and damping coefficients are investigated for the model scale and full scale to study the scale effects. The results at the model scale are compared against experimental measurements and good correlation was found.
Controlling the roll motion of a ship in a seaway is essential for the safety and habitability. The roll motion of a ship is nonlinear, and the nonlinearity increases at the resonance as the ship experiences larger roll motion. Accurately computing the roll damping at the resonance frequency is important because the moment of inertia and restoring moment counteract each other and the damping moment opposes the roll motion. The total roll damping consists of friction damping, body eddy shedding damping, surface wave damping, lift force damping, and appendages damping. The wave and lift force damping can be calculated by potential flow theory based methods, whereas others are influenced by viscosity.
In general, most roll damping calculation methods are based on empirical models, and Ikeda's method (Ikeda et al. 1978) is most common one. Although this method works quite well for conventional ships, the predicted results are sometimes conservative or underestimated for unconventional ships (Gu et al. 2013). Large roll damping is strongly nonlinear and is influenced by fluid viscosity and flow characteristics such as flow separation and vortex shedding. Empirical or semi-empirical methods cannot account the flow characteristics of such a complex flow. Roll damping calculation for conventional ships by Ikeda's simplified method can fit experimental data quite well at small roll angles. However, when the roll angle is large, it is out of the acceptable range of Ikeda's method, and the accuracy of the computed damping coefficient is low (Kawahara et al. 2012).