A motion prediction method for damaged ships in waves considering internal flooding flow

Objectives To reduce the computational cost of predicting flooding and wave-induced motions of damaged ships, a fast 6+N-degree-of-freedom time-domain coupled method is developed by combining three-dimensional potential-flow theory with an equivalent lumped-mass model.

Methods Physical model tests are used to assess calm-water flooding responses and intact-ship motions in waves. For small-opening flooding in waves, where directly corresponding test data are unavailable, numerical cross-comparisons are conducted with computational fluid dynamics (CFD) results.

Results For the calm-water two-compartment flooding case, the relative error between the maximum roll amplitude predicted by the simplified method and the experimental result is 3.6%. For the small-opening case with H/λ = 1/50, the simplified method reproduces the CFD-predicted oscillations in flooding mass and the overall trends of roll and heave, although a noticeable discrepancy remains in the heave amplitude. In the intact-ship validation case with H/λ = 1/50, the relative error of the roll Response Amplitude Operator(RAO)predicted by the simplified method increases to 9.3%, indicating limitations of the linear potential-flow hydrodynamic approximation under relatively strong nonlinear wave conditions.

Conclusions For a representative small-opening case in regular waves, the simplified program requires approximately 1.5 s to simulate 20 s of physical motion, whereas the corresponding CFD simulation requires approximately 20 h. The proposed method is therefore suitable for rapid screening and response-trend assessment of flooding and ship motions under regular-wave small-opening conditions. However, its quantitative predictive accuracy under large wave steepness, strong shallow-water sloshing, and other complex nonlinear flow conditions requires further validation.