## 3 Results
### Performance Variation with Slit Height and Jet Injection Volume
Therefore, as \(C_{j}\) increased at all slit heights, so did the wall shear stress. Therefore, unlike Figure 14b, it can be confirmed in Figure 17b that the lower the slit height, the more the torque on the blade tended to increase. Figure 17: \(10\text{K}_{\text{Q}}\) according to \(C_{j}\) for each part of the propeller with each slit height (\(J_{A}=0.4\)). Figure 18: \(Cont\). Figure 19 shows the distribution of torque PUA generated in the inner structure. The surface in the leading edge direction is defined as \"outside,\" and the surface in the trailing edge direction is defined as \"inside.\" When \(h_{S}\) = 1.0 mm, the jets are concentrated at high r/R, as described above, which greatly reduces the torque in the round tunnel at outside. However, in the case of the tunnel, the torque generation area is not large compared to other propellers. At \(h_{S}\) = 0.6 mm, compared to \(h_{S}\) = 1.0 mm, the jet injection is dispersed throughout the slits, and the torque does not decrease significantly in the round tunnel. Even in the case of tunnels, torque appears in a relatively large area compared to \(h_{S}\) = 1.0 mm. At \(h_{S}\) = 0.2 mm, as explained earlier, the slit area is narrow, and the pressure inside the inner structure increases. As a result, depending on the direction of the round tunnel, negative torque is generated in the round tunnel at outside, and positive torque generated in the inner round tunnel, which cancel each other out. In order to inject a jet, additional power is required from the pump. In order to calculate the power of the pump, the head (\(H\)) of the pump must be considered. The head is the energy of a fluid of unit weight and can be expressed as in Equation (10). \[H=H_{p}+H_{v}+H_{l} \tag{10}\]  
The potential head (\(H_{p}\)) is the difference between the potential energy of the inlet and the potential energy of the outlet in the propeller structure, which is the same as the  
Figure 19: Torque PUA distribution of inner structure at \(C_{j}\) = 0.125. Figure 18: Distribution of torque PUA according to \(C_{j}\) for each slit height (\(J_{A}\) = 0.4). difference in the depth of the inlet and outlet. The velocity head (\(H_{\rm{p}}\)) also is the difference in kinetic energy between the inlet and outlet. Finally, the head loss (\(H_{\rm{I}}\)) is the energy that the fluid flowing in the internal structure loses by friction or collision with the wall surface. In this study, for simple comparison, it is assumed that the depths of the inlet and outlet in the propeller structure are the same, and the there is no energy loss due to friction or collision with the wall surface. Therefore, the head of the pump required to inject the jet is considered only with the velocity head and can be calculated by Equation (11). \[H=\frac{V_{jet}^{2}}{2g} \tag{11}\]  
Figure 13:0  
Using the head of pump obtained in Equation (11), the power of the pump can be obtained as in Equation (12). \(\alpha\) is the margin ratio, and \(\eta_{Pump}\) is the efficiency of the pump. In this study, the margin ratio is assumed to be 0, and the pump efficiency is assumed to be 1 for simple comparison. The efficiency of the propeller considering the power of the pump is the same as in Equation (13). Figure 13:1  
Table 6 shows the change in propeller performance due to the slit height and \(C_{j}\). Compared with the condition not injecting a jet, the difference of \(K_{T}\) and \(10K_{Q}\) at each \(C_{j}\) is compared. Low \(C_{j}\) has the highest increases in thrust by inducing a downwash across the slit at high jet speed. However, as the results confirmed earlier, as \(C_{j}\) increases, \(\Delta K_{T}/C_{j}\) increases when the jet thickness is thick (\(h_{S}=0.6\) mm and \(h_{S}=1.0\) mm). Even with the same \(C_{j}\) (that is, the momentum of the jet injected from the slit is the same), the thrust increase appears different depending on the hydrofoil geometry of high curvature and thickness of the jet.