The objective of this research is to model the physics of the separated unsteady viscous flow over the bilge keels of an FPSO hull subject to roll motions. A cell center based Finite Volume Method (FVM) scheme is implemented for the solution of the 2-D Navier-Stokes equations (NS2D). The scheme is verified in the case of a submerged fixed hull with bilge keels subject to alternating flow. The effects on the pressure distribution along the hull and the moment histories are investigated. Moreover, the inviscid flow results are also compared to those from the Boundary Element Method (BEM) based potential solver for verification purposes.


FPSO hulls have often been found to be subject to excessive roll motions. The installation of bilge keels has been widely used as an effective and economic way of mitigating the roll motions of hulls.

Vugts (1968) was the first to calculate the hydrodynamic coefficients for sharp-edged sections in roll motions and observe the importance of viscous effects. Yeung, Liao, and Roddier (1998) applied the Free- Surface Random Vortex Method (FSRVM), Yeung and 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. They also suggested a composite model for extracting the hydrodynamic coefficients from the roll moment history. Yeung, Roddier, Liao, Alessandrini, and Gentaz, (2001) included the effects of bilge keels in the case of an FPSO hull subject to roll motion by using the FSRVM and compared the results to those of a Boundary-Fitted Finite Difference Method (BFFDM, Alessandrini and Delhommeau, 1995) and those measured in their experiments. Their numerical solutions show that an increase in the keel size increases both the added mass and damping coefficients.

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