A finite volume method-based Navier-Stokes solver is developed for the prediction of the flow around hull sections in roll motion. The corresponding hydrodynamic loads on the hull are determined, and the results are compared with published experimental data. The present method is applied to several hull shapes subject to prescribed roll motions or in transient roll-decay motions. It is found that, due to the effects of viscosity, the results are nonlinear with roll angle, even for small angles. From the analyzed hull geometries, the one with 4% bilge keels was found to be the most effective in reducing roll motions.
Ship-shaped hulls have often been found to be subject to excessive roll motions, which inhibit their use as a stable and uninterrupted production platform. Bilge keels have been used widely as an effective and economic way of mitigating roll motions over a large range of frequencies. The performance of a hull subject to roll motions is measured, conventionally, in terms of hydrodynamic added-mass and damping coefficients. Vugts (1968) was the first to measure and calculate the hydrodynamic coefficients on hull sections (without bilge keels) in roll motion, and to point out the importance of the effects of viscosity. The estimation of these coefficients through various numerical methods and validation through experiments has been the focus of research over the years (Na et al., 2002; Wilson et al., 2006; Yeung et al., 1998; Yeung et al., 2000). Yuck et al. (2003) investigated experimentally the prediction of the damping coefficient on a nonconventional hull section, where they found that the roll damping could change significantly due to hull geometry. A 2-dimensional Navier-Stokes solver (NS2D) was developed By the Ocean Engineering Group (OEG) of the University of Texas at Austin based on Choi (2000), Choi and Kinnas (2001, 2003), and Kinnas et al. (2003).