## 3 Results and Discussion
### Open Water Performance  
The open water performance comparison between the ducted propeller and the RDT is given in Figure 6, in which the propeller thrust coefficient, \(K_{tp}\), duct thrust coefficient, \(K_{tn}\), propeller torque coefficient, \(K_{qp}\), and overall coefficients, \(K_{t}\), \(K_{q}\) and efficiency are shown based on the hydrodynamic coefficient definitions as mentioned before. The green curves represent the hydrodynamic coefficients for the ducted propeller and the blue curves for the RDT. For the DP, the total thrust coefficient includes the propeller thrust coefficient and duct thrust coefficient, and the torque coefficient includes the propeller torque coefficient, while, for the RDT, the total thrust and torque coefficient also include an additional term, i.e., the rim coefficient. From Figure 6a-c, in which the thrust and torque contribution from the rim is excluded for the RDT to make a clear comparison, it can be observed that the propeller thrust coefficient, duct thrust coefficient, and propeller torque coefficient for the RDT are smaller than those for the DP under all advance coefficients. In Figure 6d, it can be seen that with the thrust contribution from the rim, the total thrust coefficient for the RDT is still below the DP. On the other hand, the additional torque of the rim in the RDT makes the torque coefficient of the RDT larger than the one of the DP. The overall effect is that the efficiency of the RDT is significantly lower compared to the DP and the discrepancy increases with an increase in the advance coefficient. The maximum discrepancy is up to almost 0.18 at J = 0.7, and, at the design point, i.e., at J = 0.5, the discrepancy is about 0.15. The efficiency curve is always below 0.4 for the RDT, and in the study of [PERSON] et al. (2016) similar results can be observed, in which a smaller RDT with a diameter of 150 mm was studied and the maximum experimental efficiency was around 0.15, which may suggest that RDTs with small dimensions tend to have a poor performance. Figure 5: Validation of the numerical model in this study by the experimental results of [PERSON] et al. (2011) for the ducted propeller. The thrust and torque generated on the propeller are caused by pressure differences across the blades and viscous shear stresses. Table 3 gives an overview of the contribution of pressure and viscosity to the thrust and torque production on the propeller for two extreme off-design points. It can be seen that pressure is the dominant factor in generating both thrust and torque and that the viscous shear is similar for both the ducted propeller and the RDT. The pressure distributions on the propeller's pressure and suction side are provided in Figure 7. The pressure distribution on the suction side displays a similar pattern except for a small low-pressure region found near the leading edge at the propeller's tip for the RDT (the propeller is rotating in the anti-clockwise direction in this view). On the pressure side, the main difference can also be found near the leading edge where the location and area of the high-pressure region are slightly different (the propeller is rotating in the clockwise direction in this view). Figure 6: Open water performance comparison between the ducted propeller (DP) and the RDT: (**a**) propeller thrust coefficient; (**b**) duct thrust coefficient; (**c**) propeller torque coefficient; (**d**) overall coefficient. To quantitatively understand the pressure difference on the propeller surface of the DP and the RDT, the pressure distribution on the blade at various radial cross-sections is presented in Figure 8, in which the pressure coefficient is given as a function of the normalized chord-wise direction z. Coordinate 0 represents the center position of the propeller. It can be observed that the pressure coefficient of the RDT is generally smaller than the one of the ducted propeller at different sections.