Methods for assessing the ship rudder stability under lock-in phenomena considering fluid-structure interactions

Ship rudders, as well as other common underwater appendages, take the form of hydrofoils with a finite trailing-edge thickness to produce wake vortex shedding, which causes vibrations, due to the fluid-structure interactions. Notably, underdetermined phenomena, such as the lock-in phenomenon, raise significant concerns about the structural stability of rudders of large container ships. However, methods to accurately evaluate the stability at the lock-in region are unavailable, because of its high instability, which requires high computational costs, especially for underwater applications. In this study, to address these deficiencies, methods to estimate ship rudders’ structural response and stability at lock-in regions were developed by incorporating hybrid-coupling techniques. The effect of the lock-in phenomenon was investigated using an S-N curve and the fatigue structural-failure probability to quantify the risks. The structural response to the stability analysis was obtained using hybrid-coupling fluid-structure interaction analysis methods by preconditioning the solutions to reduce the numerical instability for first bending and twisting modes with the modified Theodorsen function and to share a single interface between the structure and flow solvers on the OpenFOAM computational fluid dynamics (CFD) toolbox. The accuracy of the structural responses was validated with experiments for the lock-in frequencies, velocity range, and, most importantly, amplitudes of the structural responses of a cantilever hydrofoil. Structural-stability analysis results using the proposed methods demonstrated a significant increase in the probability of premature structural failure, thereby demonstrating the usability of the methods by structural designers in the early design stages.