The objective of this research is to understand the physics of the separated unsteady viscous flow over the bilge keels of an FPSO hull subject to roll motions and to predict the corresponding hydrodynamic coefficients. A numerical scheme which is based on the Finite Volume Method (FVM) for the solution of the 2-D Navier-Stokes equations is presented (NS2D). The scheme is validated for a submerged hull roll problem and applied to FPSO hull subject to roll motions with or without bilge keels. The effects of the bilge keel size and orientation on the hydrodynamic coefficients are investigated. Moreover, a Boundary Element Method (BEM) based potential solver is developed in order to investigate the effects of the non-linear free-surface boundary conditions the predictions.


FPSO hulls have often been found to be subject to excessive roll motions. The installation of bilge keels has widely been used as an effective and economic way of mitigating the roll motions of hulls. Therefore, predicting the separated flow around the bilge keels and its effect on the hydrodynamic coefficients and the pressure distribution along the hull is essential in assessing the effectiveness of various types of bilge keel shapes in mitigating roll motions.

Vugts (1968) was the first to calculate the hydrodynamic coefficients for sharply edged sections in roll motions and observe the importance of the viscous effect. Yeung et al. (1998) applied the Free-Surface Random Vortex Method (FSRVM, Yeung & Vaidhyanathan, 1994) to a rectangular ship-like section oscillating in roll motions and compared the hydrodynamic coefficients obtained from their method with those obtained from their experiments. The results showed that the added mass coefficient was not affected for roll amplitudes less then 5 degrees. Yeung et al. (1998) also suggested a composite model for extracting the hydrodynamic coefficients from the roll moment history.

This content is only available via PDF.
You can access this article if you purchase or spend a download.