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.

The propulsion performance and propeller design of ships have traditionally been evaluated mainly under calm-water conditions. However, under actual sea conditions, waves can increase added resistance, change the stern wake distribution, reduce propulsive efficiency, and affect cavitation behavior. This study evaluates the propulsion performance and designs a propeller for an 1800 TEU container ship under regular wave conditions using computational fluid dynamics. Resistance and self-propulsion simulations are conducted for eleven wavelength ratios in the range of $0.5\le \lambda /L_{PP}\le 2.0$, with a fixed wave steepness of $H/\lambda =0.01$. The results show that the required power increases significantly in the resonance wavelength range because of the combined effects of added resistance, wake variation, and reduced propulsive efficiency. The Brake Horsepower (BHP) transfer function obtained from the regular wave simulations is combined with representative sea-state spectra using the spectral method to estimate the Daily Fuel Oil Consumption (DFOC) under actual operating sea states. The total long term DFOC is estimated as 37.084 t/day. For the propeller design, the wake distribution at the propeller plane is analyzed at $\lambda /L_{PP}=1.1$, as a representative wave condition where the ship motion and propulsion performance variation become significant. The wake analysis shows that the instantaneous inflow changes considerably according to the wave phase, which can affect blade loading and cavitation. Based on this analysis, a new propeller geometry is designed with the cavitation performance as the primary consideration while also improving the propulsion performance. The designed propeller reduces the cavity volume over the selected wave phases and decreases the delivered power by approximately 2.1% in calm water and 3.4% in wave conditions. These results demonstrate the importance of considering wake variation and cavitation characteristics in practical propeller design under actual operating conditions.