Numerical investigations of hydrodynamic, manoeuvring dynamics and empirical coefficient sensitivity of free-running vessels in stern quartering seas

• A reduced fidelity, time-domain simulation program is developed to study manoeuvring in astern waves, unifying a seakeeping model, which accounts for forward speed effects, and a non-linear manoeuvring model. • A detailed parametric analysis is conducted, systematically varying empirical coefficients to study the sensitivity of each parameter in following seas • Effect and uncertainty of wave conditions - wave height, wave period, wave encounter angle and wave phase angle - on manoeuvres in following seas were investigated. Ships operating in following seas experience low encounter frequencies compared to head seas, making most existing numerical models less suitable for investigating hydrodynamic phenomena for ships in stern-quartering waves. While previous research has examined extreme conditions like surf riding and broaching, steering performance and hydrodynamics under typical operational conditions in following waves have received less attention. This study introduces a modular, reduced-fidelity, time-domain simulation model to analyse vessel motion in these conditions, balancing the computational efficiency and sufficient accuracy for practical use. The model is validated with the Duisburg Test Case and Mariner vessels for versatility. A sensitivity analysis was conducted using the numerical model, supported by newly conducted model experiments with an operational case vessel, providing insights into the causality of empirical coefficients and impact on steering and manoeuvring performance. Key findings suggest that the linear wave scattering loads in following seas reduce with increasing forward speeds, and the wave forces are better modelled with speed dependency. The variations in the aft flow separation section, crossflow drag coefficient, and wake fraction impact vessel motion and stability. Additionally, increased wave height and wave angle reduce directional stability in stern-quartering waves. The importance of using a complete motion profile is also highlighted.