The prediction of roll motion of a ship with bilge keels is particularly difficult because of the nonlinear characteristics of the viscous damping. Flow separation and vortex shedding caused by bilge keels significantly affect the roll damping and the magnitude of the roll response. To predict free response of roll, the Slender-Ship Free-Surface Random Vortex Method (SSFSRVM) developed in Seah & Yeung (2008) [1] was employed. It is a fast free-surface viscous-flow solver designed to run on a standard desktop computer. It features a quasi-three dimensional formulation that allows the decomposition of the three-dimensional hull problem into a series of two-dimensional computational planes, in which the two-dimensional free-surface Navier-Stokes solver FSRVM [2] can be applied. This SSFSRVM methodology has recently been further developed to model multi-degrees of freedom of free-body motion in the time domain. In this paper, we will first examine the effectiveness of SSFSRVM modeling by comparing the time histories of free roll-decay motion resulting from simulations and experimental measurements. Furthermore, the detailed vorticity distribution near a bilge keel obtained from the numerical model will also be compared with the experimental PIV images. Next, we will report, based on the time-domain simulation of the coupled hull and fluid motion, how the roll decay coefficients and the flow field are altered by the span of the bilge keels. Plots of vorticity contour and vorticity iso-surface along the three-dimensional hull will be presented to reveal the motion of fluid particles and vortex filaments near the keels.

It is appropriate and an honor for me to present this roll-damping research in the Emeritus Professor J. R. Paulling Honoring Symposium. It was from “Randy” that I first acquired the concept of equivalent linear damping. Even more so, I am very grateful for his teaching, guidance and friendship of many years. — R. W. Yeung

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