Numerical and experimental investigation of rudder-induced hydrodynamic forces on an inland waterway ship in deep and shallow waters

This study presents an in-depth experimental and numerical investigation of hydrodynamic forces induced by high-lift rudders on an inland waterway ship operating in medium deep and shallow water. A model scale representation of the real motor ship (MS) Monika Deymann, equipped with two axisymmetric ducted propellers and two twin high-lift rudders, was tested in captive conditions at two water depth-to-draft ratios (h/T), in medium deep water at h/T=2.0 and shallow water at h/T=1.2, in quasi-steady straight-ahead, rudder, and combined drift–rudder conditions. The Reynolds-averaged Navier–Stokes (RANS) equations were solved using two techniques for the propeller rotation: steady Moving Reference Frame (MRF) and unsteady Sliding Interface (SI). Closure of the equations was achieved using the Reynolds Stress turbulence Model (RSM). The unsteady RANS SI method achieved better overall agreement with the experimental measurements, showing deviations of 5.81% for yaw moments, as opposed to 21.63% for the steady MRF approach, both at 45° rudder deflection. Our results demonstrated that the water depth restriction substantially amplified rudder-induced hydrodynamic forces, with lateral forces increasing by up to 50.53% at h/T=1.2 compared to h/T=2.0 at the stall angle of δ=45°. The flow analysis revealed enhanced separation zones and asymmetric pressure distributions in shallow water, with rudders contributing up to 81.0% of total yaw moments. These findings confirm that high-fidelity unsteady numerical modeling is essential to capture shallow water effects and provide a foundation for developing more accurate rudder models and control algorithms for predicting the maneuverability of inland waterway ships operating in restricted waterways.