Roll damping is an input parameter for the second-generation intact stability criteria and is also a key factor for predicting large roll motions and capsizing in waves, accurately estimating roll damping is still a challenging task with large roll motion. In order to provide a reliable method for predicting roll damping, this paper uses the unsteady RANS equations combined with the VOF method. A numerical method for simulating harmonic forced roll motion with different forward speeds is established by using overset grid approach. The accuracy of the method is verified by existing experimental data, and the influences of rudder and bilge keels are studied by varied forward speeds, roll amplitudes and roll periods. The results show that the rudder and bilge keels contribute noticeably to roll damping with higher speed and larger roll amplitude, and the bilge keel interacts with free surface leads to the error increasing between the simulation and experiment.


A ship may occur extreme roll motion in severe waves and winds condition, thus leading to large amplitude roll motion. Large roll angles and accelerations can cause significant crew inefficiency and reduce the stability of the hull, or leading to capsizing. A sufficient roll damping moment prevents the dynamic loss of stability, and roll damping is also fundamental in case of the majority of failure modes addressed by Second Generation Intact Stability Criteria, thus the accurate prediction of roll damping of ships is particularly important.

At present, the estimation of roll damping is both challenging as well as an extensively studied problem. Usually, there are three methods to evaluate the roll damping: semi-empirical approach, model test and numerical simulation. The most popular semi-empirical method is a component-based method, which considers the physical processes of roll motion damping with various means of energy dissipation, including friction, lift, wave-making, and vortex generation from the hull, as well as the influence of appendages (Ikeda, et al., 1978; Himeno, 1981). Unfortunately, the range of application is limited in most extreme roll motions. Different techniques of model test exist to estimate roll damping, which are roll decay motion, harmonic excited roll motion and harmonic forced roll motion. Roll decay and harmonic excited roll based on roll angle measurements make the comparison of the roll damping coefficient between experiment and simulation difficult. Roll decay is a fully non-stationary harmonic process, the initial state and higher Froude number have a strong influence on the test results. Considering the rudder is used to hold the model on course in harmonic excited roll motion, the propeller-rudder interaction adds the complexities for the model test. The fixed roll axis of harmonic forced roll motion and the direct determination of the moment make it easier to measure roll period and amplitude. In this paper, we focus on the harmonic forced roll motion to validate the established numerical methods. Besides model tests, the development of high-performance computers promotes the work for estimating roll damping numerically. Finite volume methods seem to be appropriate to simulate the roll damping coefficients and flow characteristics visually.

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