Numerical Investigation of Maneuvering Characteristics for a Submarine Under Horizontal Stern Plane Deflection in Vertical Plane Straight-Line Motion

The maneuverability of a submarine in the vertical plane is a key indicator of navigation safety. However, existing studies typically evaluate maneuvering performance based on hydrodynamic coefficients, often neglecting the flow-field evolution induced by different steering strategies. In this study, a high-fidelity numerical model for the vertical-plane motion of the DARPA SUBOFF submarine is established using the Reynolds-Averaged Navier–Stokes (RANS) method and validated against benchmark data. Unlike traditional analyses that employ a fixed rudder angle, this work systematically compares three steering strategies with continuously varying rudder angles—trapezoidal, step, and linear steering—examining their motion responses, hydrodynamic performance, and unsteady flow-field evolution. The results show that, although step steering produces the fastest response with the strongest transient characteristics, it also triggers pronounced flow separation and significant unsteady effects. Linear steering yields a smoother but the weakest motion response, with reduced rudder effectiveness and a noticeable lag effect. In contrast, trapezoidal steering maintains a stable flow field around the submarine, with uniformly concentrated vorticity distribution, ensuring smooth and safe motion and achieving a favorable balance between response speed and flow stability. The findings provide theoretical reference for research on submarine vertical-plane steering motion, rudder-angle control, and flow-field stability.