Abstract The main purpose of the present study is the develop- ment of a simple and reliable numerical tool that can be used for modeling the separated flow field around a ship in roll motion and to estimate the associated vortex roll damping coefficients。 A numerical method based on the DVM (Discrete Vortex Method) has been developed。 The roll motion is modeled by a distribution of sources on the sectional hull surface。 Vorticesare introduced into the flow to represent flow separation。 The roll mo- ments and viscous roll damping coefficients are pre- dicted by the developed model and are applied to pre- dict the roll R。A。O (Response Amplitude Operation) for a barge and the Series 60 hull。81958

Keywords DVM; Vortices; roll motion; R。A。O; barge; Series 60。

1。Introduction

The assessment of the wave-induced motions of a ship is an essential part of the early ship design process。 The wave excitation and motions of a ship can be estimated by the use of linear potential flow theory (Lloyd, 1998)。 For these estimations, viscous effects are usually ne- glected and it is assumed that the flow is maintained around body without separation。 In particular cases, if ship is in the roll motion with relatively sharp edges, the viscous effects associated with flow separations from its edges can make significant contributions on the relative motion predictions (Downie et al, 1993)。

The total hydrodynamic damping in roll motion can be obtained by summing up the wave radiation and viscous damping。 The estimation of viscous roll damping isnot

allows very accurate prediction of ship behavior in most motion situations。 However, it is questionable whether this is a suitable tool for use at the early design stage, mainly due to the costs and the time involved and the fact that hull geometry may not be sufficiently deter- mined at that stage to allow models to be constructed and tested。

The present study is concerned with the development of the simple and reliable numerical tool, so that it can be used for the practical purpose of the prediction of sepa- ration flow fields and the associated vortex roll damping coefficients for various hull forms in roll motion。 The discrete vortex method provides an effective way to account for the effects of vortex shedding in the poten- tial calculations。 The roll motion is modeled by distribu- tion of sources on the hull surface。 Vortices are intro- duced into the flow to represent flow separation。 The calculation is carried out on a grid based fluid domain and the velocities of each time steps are calculated at the grid nodes using Biot-Savart low。 A generalized trans- formation is employed so that simple hull sections and other more ship like hull forms can be treated。

The roll moments and viscous roll damping coefficients are predicted by the developed model and are applied to predict the roll R。A。O of various hull forms。 The calcu- lated viscous roll damping coefficients are compared with the existing experimental results to validate the model being developed。 The results to be presented are for the wall side barge and the Series 60 Cb= 0。6 hull。

2。The Discrete Vortex Model

If the flow around an each hull section is considered as two-dimensional and incompressible, the governing equation can be expressed in terms of the vorticity transport equation,

easy using conventional potential methods, andusually

estimated by experiments (Brown et al, 1983) or semi-

empirical method that are based on analysis of the ex- perimental data (Himeno, 1981; Ikeda et al, 1977)。 Model testing, coupled with simulation techniquesnow

u is the velocity。 The vorticity is

The discrete vortex method represents vorticity in the flow by arrays of discrete vortices in an otherwise irro- tational fluid and calculates its convection using the Biot-Savart law。

2。1Hull Transformation。