Pure loss of stability prediction in following waves incorporating hydrodynamic lift force effect

When ships navigate in following waves, they are often accompanied by nonlinear phenomena such as a significant reduction in roll restoring force caused by changes in waterplane area, and unintended acceleration induced by excessive surge force. These phenomena are likely to trigger intact stability failures involving large-angle heel, such as pure loss of stability, in which the current motion prediction accuracy is not adequate. To further investigate the mechanism of nonlinear roll motion of pure loss of stability in following waves, a numerical method for a six-degree-of-freedom (6-DOF) weakly nonlinear time-domain model based on the unified theory is developed. This method not only couples the dynamic characteristics of seakeeping and maneuvering but also incorporates the hydrodynamic lift force via the Vortex Lattice Method (VLM) to characterize the lateral fluid effects induced by variations in heel angle and ship speed. To address the issue that the VLM may lead to overestimation of the lift force, Computational Fluid Dynamics (CFD) method is employed to conduct quantitative analysis on the vortex shedding behavior of the ship under self-propulsion conditions, thereby correcting the lift force calculated by the VLM. Comparisons between the predicted results of the modified 6-DOF model and published model test data indicate that as the ship speed increases, the lift force exerts a significant amplifying effect on the ship's roll response. Moreover, the correction of the lift force can effectively improve the predictive accuracy of the 6-DOF model. This study clarifies the influence of the lift effect on the nonlinear roll motion of ships in following waves, verifies the effectiveness of the 6-DOF weakly nonlinear model based on "VLM + CFD correction" in predicting ship roll motion, and provides technical support for ship stability assessment and the formulation of navigation strategies.