Numerical Investigation of Coupled Oblique Flow and Steering Effects on Hydrodynamic Performance of Rudder Behind Propeller

The hydrodynamic performance of a rudder behind a propeller is critical for determining vessel maneuvering stability. During navigation, the coupled effects of the oblique flow angle (β) and the rudder angle (δ) significantly alter the wake velocity field and vortex patterns aft of the rudder. However, the synergistic control mechanism of these two variables requires further quantitative investigation. This study employs the RANS method with the SST k-ε turbulence model to numerically simulate flow under advance coefficients (J) ranging from 0.3 to 0.9, oblique flow angles (β) from 0° to 15°, and rudder angles (δ) from 0° to 35°. Hydrodynamic coefficients, including the lift coefficient, drag coefficient, and lift-to-drag ratio, were calculated for the rudder. The evolution of the horizontal velocity and vortex fields was captured, with the model validated through localized flow field visualization. The results reveal that when β ≤ 3°, δ is the dominant factor influencing rudder hydrodynamics. Conversely, when β ≥ 9°, β becomes the primary regulating factor. The coupling effect induces significant asymmetry in the velocity distribution across the rudder surfaces and pronounced flow separation on the windward side, generating a complex vortex system (including primary and secondary vortices) on the leeward side. This research elucidates the coupled control mechanism of oblique flow and rudder angle, providing insights for enhancing steering margins and a quantitative foundation for optimizing rudder profiles in challenging sea environments characterized by high oblique flow and large rudder angles.