## 2 Experimental and Numerical Method  
### Propeller Modelling  
The profile of the propeller blade in this study is based on a NACA66 airfoil, which is widely used as a section of ship propellers such as the KP505 [17] and KP632 [18]. The section of NACA66 (MOD) used in this study is shown in Figure 1. Additional structures were added inside the hydrofoil to inject a jet. In order to secure the strength of the experimental equipment, the thickness of the NACA66 (MOD) is set to 24% of the chord length.  
Figure 1: NACA66 (MOD, t/c = 0.24) geometry with jet and without jet.  
In Figure 1, the tunnel is the passage through which water flows from the shaft to the propeller blades to inject a jet. The slit is the jet opening in the hydrofoil, and the round tunnel is the passage connecting the tunnel and the slit. In the case without a jet section, since a jet is not injected, only the tunnel exists inside the hydrofoil. In the geometry with a jet section, the slit, round tunnel, and tunnel exist inside the hydrofoil to inject the jet. This section is designed without an angled part as possible in the hydrofoil after the slit so that the jet injected from the slit can flow along the hydrofoil.  
In addition, in the case with a jet section, all hydrofoil geometry except around the slit was made with the same geometry as without a jet section. The shape and location of the slit and tunnel were selected based on [PERSON] et al. [16], who optimized the shape of the jet nozzle through 2D and 3D hydrofoil studies that injected a jet. The position of the slit is in the center of the chord, and the height of the tip was selected as 25% of the slit height.  
Based on the NACA66 (MOD, t/c = 0.24) section in Figure 1, a Coanda propeller that injects a jet from the propeller blade surface was manufactured. The specifications of the propeller are shown in Table 1. The diameter of the propeller \((D)\) is 250 mm, which is relatively large compared to other propellers to make inner structure, and the length of the chord \((c)\) is 50 mm. The geometry of the propeller was designed as a simple shape with only pitch without rake and skew as a basic study.  
Figure 2 shows the propeller used in the experiment and the modeled propeller. It also shows the shape of the inner structure. The Coanda propeller used in the experiment was manufactured through 3D printing using acrylic material to secure the strength of the propeller. When manufacturing the propeller, the height of the slit was selected as 1.0 mm in consideration of the manufacturing limit of the 3D printer equipment. Slit smaller than 1.0 mm could not be manufactured through 3D printing, so the performance change according to the slit height was studied through numerical computations.  
The propeller shaft was designed as a hollow shaft so that the water required for jet injection could have a passage through which it can move. The hollow shaft is called the inner tunnel, and its diameter is 0.144 \(D\), which is about 57% of the entire hub diameter.  
From the inner tunnel to the propeller r/R = 0.5, it consists of the without a jet section, allowing water to rise up to the slit. From r/R = 0.5 to 0.9, the propeller is composed of with a jet section, and jets are injected through a lit. There is no tunnel inside the section above r/R = 0.9 because water does not need to move there.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Diameter, \(D\)(mm) & 250 \\ Pitch ratio, \(P/D\) & 0.777 \\ Hub ratio, \(d/D\) & 0.250 \\ Inner tunnel ratio, \(d_{inner}/D\) & 0.144 \\ No. of Blades & 2 \\ Section Section & NACA66 (MOD, t/c = 0.24) \\ Slit position (r/R) & 0.5–0.9 \\ Slit height, \(l_{S}\) (mm) & 1.0 \\ Slit area, \(A_{S}\) (mm\({}^{2}\)) & 48.663 \\ Expanded area ratio & 0.186 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the Coanda propeller used in the experiment.