Determination of linear and nonlinear roll damping coefficients of a ship section using CFD

Abstract

The most prevalently used method to obtain the nonlinear roll damping coefficient is the free roll decay test. However, this method can only be conducted at the resonance frequency and thus cannot consider the effect of the frequency. This is a certain limitation as the resonance frequency can be changed at any time by the ship’s loading conditions. Therefore, it is worth investigating the frequency dependency of the nonlinear roll damping coefficients. In this study, a numerical method was proposed to derive the linear and nonlinear roll damping coefficients of ships at different frequencies. Fully nonlinear CFD simulations of forced harmonic roll motion were conducted and the roll damping coefficients were calculated. Then, the damping coefficients were decomposed into the linear and nonlinear components using the linear regression analysis. The linear roll damping coefficients were compared with potential coefficients and showed a good agreement, while the nonlinear roll damping coefficients were compared with the coefficients calculated using a semi-empirical method. The nonlinear roll damping coefficients calculated from the proposed method showed a strong frequency dependency. Finally, possible rationales for the frequency dependence of the nonlinear roll damping coefficient were investigated.