## 3 Results
### Performance Variation with Slit Height and Jet Injection Volume  
Propellers with the slit heights of 0.2 mm and 0.6 mm were designed to analyze the change in performance according to the slit height. Figure 12 shows the geometry of the hydrofoil for each slit height. The injection range is the same for all three propellers at r/R = 0.5 to 0.9, and the shape of the propeller is slightly different around the slit depending on the height of the slit. The remaining shapes are all the same. The computations were performed while changing \(C_{i}\) in order to evaluate the change in performance according to the injection volume. Table 5 shows the computation conditions for each slit height. Since the injection range is constant even if the height of the slit changes, the slit area is proportional to the scale of the slit height (\(\lambda\)). \(C_{j}\) is the product of \(\dot{m}\) and \(V_{jet}\) in Equation (1), so \(V_{jet}\) is proportional to \(1/\sqrt{\lambda}\), and \(\dot{m}\) is proportional to \(\sqrt{\lambda}\). Figure 13 shows the names of each part of the Coanda propeller. The slit, round tunnel, and tunnel are combined into an inner structure, and all the remaining parts of the propeller except the inner structure are called a blade. We compared the thrust and torque for each. Figure 14 shows \(K_{T}\) according to \(C_{j}\) for each slit height. It can be confirmed that the thrust increases for all the slit heights as \(C_{j}\) increases. In the case of the inner structure, the thrust does not differ greatly depending on the height of the slit. Naturally, most of the thrust generated by the propeller occurs from the blade. \begin{table}
\begin{tabular}{c c c c c c} \hline \  
When the jet is not injected, the highest thrust is displayed at \(h_{S}\) = 0.2 mm, which is a phenomenon manifested by the hydrofoil shape. Looking at Figure 12, there is a part where the hydrofoil is cut by the slit in the with jet section. The lower the slit height, the more the existing hydrofoil shape will be maintained, so most will appear when the jet is not injected in the lowest slit height. However, although the thrust increase appears differently depending on the slit height, most thrust appears when \(C_{j}\) = 0.2 and \(h_{S}\) = 1.0 mm. Figure 15 shows the thrust PUA and velocity distribution of the propeller surface by \(C_{j}\). Only the negative tangential velocity contour is shown for convenience to see the jet distribution. The jet injection distribution is different according to the slit height. When \(h_{S}\) = 0.2 mm, it can be confirmed that the jet injected from the slit is generated in a narrow ad fast flow, and the jet rides to the end of the blade, where it does not separate due to the Coanda effect. In addition, the small slit area increases the pressure of the inner structure, resulting in a pattern in which jets are injected from the entire slit. In contrast, when the height of the slit is increased, the area of the slit is increased, and the jet injection velocity is reduced. As a result, the Coanda effect causes the jet to flow on the blade, but it is relatively separated and disappears quickly. The jet injection pattern is also concentrated at high r/R due to the centrifugal force caused by the rotation of the propeller. Figure 14: \(K_{\rm T}\) according to \(C_{j}\) for each part of the propeller with each slit height (\(J_{A}\) = 0.4). Figure 13: The names of each part of the Coanda propeller. It can be confirmed that the lower the height of the slit, the closer the region where the thrust is generated is to the slit. Looking at Figure 12, there is a surface that is cut so that the jet injected from the slit can flow on the hydrofoil surface. This surface has a larger curvature as the height of the slit increases. When a jet is injected, downwash is induced at this part due to the Coanda effect, thrust is generated at the surface that is cut. It can be seen that the downwash induced in the front of this slit increases as \(C_{j}\) increases.