## 3 Results
### E1619 propeller in Open Water Test  
In contrast to KP505 and Section 3.1, this section will investigate a propeller with a short chord length, i.e., a small EAR (expanded blade area ratio) and available for a 3D geometry model instead of an offset table. The seven-bladed and highly skewed submarine propeller E1619 was chosen. The main particulars are shown in Table 8. Its 3D model was provided by INSEAN (Italian Ship Model Basin), and the 2D geometry outline was extracted using Equations (10)-(15). The CFD setup and grid system are exactly the same as the one used in Section 3.1. This is also proof of the high flexibility of the presented propeller model; it is convenient and easy to switch between not only two body force propeller models but also different propeller geometries.  
For \(J=0.8\), the CFD using the presented blade rotating blade propeller model predicts \(KT=0.205\). Against the experimental \(KT=0.218\), the error \(E\%D\) is around 6% underpredicted. Figure 14 illustrates the axial velocity distribution directly following the propeller plane. To compare the result in Figure 14, please refer the Figure 4.13 on p. 36 in [49]. The area of high velocity behind each blade body is described well for real propeller simulations (CFDSHIP-IOWA using overset grid) [49], LDV experiments [49], and the proposed rotating blade propeller model. The velocity drops between the two blades are captured as well.  
However, when using the rotating blade propeller model the lower velocity area outside the propeller radius next to each blade tip is not clear for the E1619 propeller (Figure 14). In contrast, it is clearer for the KP505 propeller in Figure 15. It can also be observed clearly in the real propeller simulation [49] and the LDV experiment [49]. Because of the small chord length and expanded blade area ratio of E1619, the grid numbers across  
Figure 13: Vortex shedding (right-wise rotation) for KP505 propeller (\(J=0.7\)).  
\begin{table}
\begin{tabular}{c c} \hline \hline Number of blades & 7 \\ Diameter (mm) & 485 \\ Hub diameter ratio & 0.226 \\ Pitch at \(r/R=0.7\) & 1.15 \\ Chord length (mm) at \(r/R=0.75\) & 6.8 \\ \hline \hline \end{tabular}
\end{table}
Table 8: E1619 propeller particulars.  
its narrow tip are less than can be covered by that of the KP505. The grid number is insufficient to adequately resolve the flow field phenomena. This issue will be investigated by a finer grid in the future.  
The propeller downstream vector field was presented in Figure 16 for the rotating blade model. Due to lack of an experimental vector field, the PIV measurement behind a submarine with an X-rudder [50; 51], e.g., Figure 13 in [51], could be used a reference for a brief comparison. A submarine is a slender body and the rudder is outside the propeller radius. Both results show that the vector directions are twisted in front of the blade's leading edge in the propeller's rotational direction. The vectors pointing to the propeller center change to the propeller's rotational direction around 0.7 \(R\). The axial velocity increases  
Figure 14: E1619 axial velocity distribution at \(x=0.17R\) behind the propeller for the rotating blade model. The propeller center is at \(x=0\). The arrow points out the low-velocity region outside blade tip.  
Figure 15: KP505 axial velocity distribution at \(x=0.0.098R\) behind the propeller for the rotating blade body model. The propeller center is at \(x=0\). The arrow points out the low-velocity area outside blade tip.