## 3 Results and Discussion
### Open Water Performance
In addition, the overall pressure difference on the propeller's pressure and suction sides for the RDT is also smaller compared to the ducted \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Advance Coefficient**} & \multirow{2}{*}{**Contributor**} & \multicolumn{2}{c}{**DP**} & \multicolumn{2}{c}{**RDT**} \\ \cline{3-6}  & & **Thrust (N)** & **Torque (N-m)** & **Thrust (N)** & **Torque (N-m)** \\ \hline J = 0.1 & Pressure & 97.41 & 3.87 & 90.5 & 3.56 \\  & Viscous & \(-\)2.05 & 0.43 & \(-\)1.99 & 0.4 \\  & Pressure & 46.57 & 2.01 & 41.45 & 1.83 \\  & Viscous & \(-\)2.16 & 0.44 & \(-\)2.11 & 0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contribution of pressure and viscosity to the thrust and torque on the propeller. Figure 7: Comparison of the pressure distribution on the propeller’s (**a**) suction side for the DP, (**b**) suction side for the RDT, (**c**) pressure side for the DP, and (**d**) pressure side for the RDT at J = 0.1.  
propeller, which explains the lower thrust production. It is noted that for r/R = 0.2 and 0.4, namely the areas near the propeller blade root, the discrepancy for the pressure difference between the pressure and the suction sides is mainly situated near the propeller's leading edge, where the highest pressure can be found. However, for r/R = 0.6 and 0.8, namely near the propeller's blade tip, the discrepancy for the pressure difference extends almost along the entire chord length. To examine the thrust difference on the duct for the DP and the RDT, the pressure distributions at three representative sections along the longitudinal direction of the duct are studied, in which the rim is not included for the RDT. The locations of these sections are situated at the propeller's leading edge, middle plane, and trailing edge, as indicated in Figure 9a. The figures exhibit the pressure coefficient as a function of position along the duct's normalized chord-wise direction, where position 0 corresponds to the location of the propeller. It can be seen that the pressure distribution on the duct's exterior side is nearly the same for both the DP and the RDT and that the pressure discrepancy is mainly situated on the interior side of the duct. Near the leading edge, the pressure difference between the DP and the RDT is not so obvious; however, at the middle plane and the trailing edge,  
Figure 8: Comparison of the pressure distribution on the blade’s radial cross-sections at: (**a**) r/R = 0.2; (**b**) r/R = 0.4; (**c**) r/R = 0.6; and (**d**) r/R = 0.8 at J = 0.1.  
the pressure difference for the ducted propeller is significantly larger than that of the RDT, resulting in a larger thrust. It can also be noted that at the interior side of the duct there are two sudden changes in pressure, which are caused by the rim gap. There is always a steep change in pressure near the blade location (Coordinate 0) for the DP because of the huge pressure gradient between the propeller's pressure and suction sides. However, for the RDT, the pressure gradient in the rim gap along the axial direction remains almost constant, which is expected for Couette flow.