Hydrodynamic Roll Predictions by Using URANS Method Combined with a Rigid Body Motion Equation

Abstract

An Unsteady Reynolds-Averaged Navier-Stokes (URANS) method is applied to the time domain simulation of roll motions of a rectangular structure and ship models in conjunction with a two-phase Volume of Fluid(VOF) approach for the free surface treatment. The roll motion of a floating structure is computed by solving the equations of rigid body motion combined with the general ship hydrodynamic URANS code, WAVIS developed by MOERI/KORDI. WAVIS uses the cellcentered finite volume method for discretization of the governing equations. Convection terms are discretized using the third order MUSCL scheme and the central difference scheme is utilized for diffusion terms. To ensure divergence-free velocity field, the SIMPLE method is employed. For the validation of the present URANS-based techniques for roll hydrodynamics, the flow around a rectangular cylinder subject to forced roll motion with the free surface is simulated. The developed vortices near the bilge are clearly shown and it is known that the interaction between theses vortices and body affects the magnitude of roll damping coefficients. The linear hydrodynamic coefficients are calculated from the time domain URANS solution by extracting the Fourier coefficients of the fundamental frequency over a time period. The computed roll damping coefficients at 5.75° and 11.5° roll angles are compared with the experimental results of Vugts (1968) and also with similar experimental results by Yeung et al. (1998), as well as with the other RANS-based numerical results (Sarkar and Vassalos, 2000). The current method produces better agreement with the experimental results at 5.75° roll angle, but gives a little higher value in the low frequency range at 11.5° roll angle. Free roll decay motion of a ship without advance speed are simulated with combined with rigid body motion equation for the naval surface combatant, which has the experimental results for two different model scales (Irvine et al., 2004 and Di Felice et al