**Diego Villa \*, Andrea Franceschi and Michele Viviani**

Department of Electrical, Electronic and Telecommunications Engineering and Naval Architecture (DITEN), University of Genova, 16126 Genova, Italy; andrea.franceschi@edu.unige.it (A.F.); michele.viviani@unige.it (M.V.)

**\*** Correspondence: diego.villa@unige.it; Tel.: +39-010-335-2345

Received: 10 November 2020; Accepted: 3 December 2020; Published: 4 December 2020

**Abstract:** The proper evaluation of the Rudder–Propeller interactions is mandatory to correctly predict the manoeuvring capability of a modern ship, in particular considering the commonly adopted ship layout (rudder often works in the propeller slipstream). Modern Computational Fluid Dynamics (CFD) solvers can provide, not only the performance of the whole system but also an insight into the flow problem. In the present paper, an open-source viscous flow solver has been validated against available literature experimental measurements in different conditions. After an extensive analysis of the numerical influence of the mesh arrangement and the turbulent quantities on the rudder provided forces, the study focused its attention on the forces generated by the rudder varying the propeller loading conditions and the mutual position between the two devices. These analyses give a hint to describe and improve a commonly-used semi-empirical method based on the actuator disk theory. These analyses also demonstrate the ability of these numerical approaches to correctly predict the interaction behaviour in pre-stall conditions with quite reasonable computational requests (proper also for a design stage), giving additional information on the sectional forces distribution along the span-wise rudder direction, useful to further develop a new semi-empirical rudder model.

**Keywords:** Reynolds Average Navier–Stokes (RANS); rudder–propeller interactions; validations and verification; actuator disk theory; rudder sectional forces
