Development of Virtual Disk Method for Propeller Interacting with Free Surface

As the environmental regulations of the International Maritime Organization (IMO) become more stringent, the accurate prediction of ship propulsion performance has become essential. Under ballast conditions where the draft is shallow, the propeller approaches the free surface, causing complex phenomena such as ventilation and surface piercing, which reduce propulsion efficiency. The conventional virtual disk (VD) method cannot adequately capture these free-surface effects, leading to deviations from model propeller results. To resolve this, a correction formula that accounts for the advance ratio (J) and submergence ratio (h/D) has been proposed in previous studies. In this study, the correction formula was simplified and implemented in a CFD environment using a field function, enabling dynamic adjustment of body force based on time-varying submergence depth. A comparative analysis was conducted between the conventional VD, modified VD, and model propeller using POW and self-propulsion simulations for an MR tanker and SP598M propeller. The improved method was validated in calm and regular wave conditions. The results showed that the modified VD method closely matched the performance trends of the model propeller, especially in free surface-interference conditions (e.g., h/D < 0.5). Furthermore, additional validations in wave-induced self-propulsion confirmed that the modified VD method accurately reproduced the reductions in wake fraction and thrust deduction coefficient, unlike the overestimations observed with the conventional VD. These results demonstrate that the modified VD method can reliably predict propulsion performance under real sea states and serve as a practical tool in the early design stage.