## 3 Results  
### Comparison of Experimental and Computation Results  
Figure 7 shows a comparison of the results of the experiment and numerical computations under the condition of jet injection and the condition without jet injection. As described above, since the flow rate injected from the propeller cannot be controlled, \(C_{j}\) is not constant for each advance coefficient. In Figure 7a, it can be seen that the results of the experiment and computation are generally similar. Compared with the experimental results at high advance coefficient, the agreement is relatively high, whereas at low advance coefficient, the error tended to increase. As can be seen in Table 2, this appears to be an error that happens when an experiment is performed at low speed. In the case of jet injection, the thrust and torque tend to decrease in both the experiment and computation. As can be seen in Figure 7b, the higher the advance coefficient, the lower the efficiency is. Although the error is relatively large at the low advance ratio, the overall trend of the \(K_{T}\) and \(10K_{Q}\) curves are similar. When the trends of the jet-injected thrust and  
Figure 6: Grid convergence for \(K_{T}\) and \(10K_{Q}\). Figure 7: Propeller water test results of experiments and calculations. torque reduction are compared, the numerical analysis and the experiment shows similar trends. After that, through computation results, the cause of the decrease in thrust and torque during jet injection was analyzed. In general, when analyzing propeller performance through numerical analysis, the changes in thrust and torque are compared using pressure and wall shear stress contours. However, when a jet is injected, the flow distribution is different from that of a general propeller. Therefore, there is a limit to analyzing the performance change of a propeller using pressure and wall shear stress as in the existing method. Thus, in this study, a function of thrust and torque was created by separating the pressure and wall shear stress into x, y, and z components and superposing them. This function means the thrust and torque acting on each surface mesh. For all surface meshes, this function multiplied by the surface area \((\Delta\mathrm{s})\) of each surface mesh is summed to become the thrust and torque acting on the entire propeller. This function was expressed by the thrust per unit area (PUA) and torque PUA, thrust PUA \((T_{PUA})\) and torque PUA \((Q_{PUA})\) can be defined by Equations (8) and (9) as follows. \[T=\sum T_{PUA}\Delta\mathrm{s} \tag{8}\]  
\[Q=\sum Q_{PUA}\Delta\mathrm{s} \tag{9}\]  
Figures 8 and 9 compare the thrust PUA and torque PUA with jet injection or without it at an advance coefficient of 0.4, at which the propeller efficiency is the highest. Changes in thrust and torque are clearly shown on the suction side where the jet is injected, while there is almost no change on the pressure side. It can be confirmed that the jet injected on the suction side does not affect the pressure side. The change in thrust and torque with and without jet injection is the largest around the slit, and the change is particularly large above r\(/\)R = 0.6. When not injecting a jet, high thrust and torque occurred behind side of the slit (between the slit and the trailing edge). When injecting a jet, the area where the thrust and torque occur increased, but the maximum result has a decrease in value. Not only that, but the same tendency is also shown on the front side of the slit (between the slit and the leading edge). When not  
Figure 8: Thrust PUA distribution on the propeller surface with and without jet injection (\(J_{A}\) = 0.4). injecting a jet, the thrust and torque PUA were high on the front side of the slit, while when injecting a jet, their values were reduced. To analyze the causes, the velocity distributions in the center of the slit were compared. Figure 10 shows the tangential velocity distribution from the center of the slit from r/R = 0.5 to 0.9, where the slit exists.