## 4 Conclusions  
The rotating blade propeller model has been developed successfully based on the blade element theory and using total velocity from RANS solution. A cell search algorithm was implemented to identify the RANS grid points inside the 2D propeller geometry. The propeller computation is based on the 25% chord length position along a foil section. The body forces were distributed linearly across the chord line with a maximal value at the trailing edge and a value of zero at the linear edge. Simulations for the KP505 and E1619 propellers in open water, and the KP505 propeller behind the KCS hull were successfully conducted. Figure 20: Flow field after propeller (\(x/L=0.985\)) for the rotating blade model when the index blade is near: (**a**) 0-degree position; (**b**) 18-degrees position; (**c**) 36-degrees position; (**d**) 54-degrees position. For KP505 propeller, the results showed good agreement with experimental data and had a small error mainly in high-load conditions. The propeller thrust coefficient was predicted well by the rotating blade model. For the KP505 propeller in open water conditions, the absolute error of the thrust coefficient was generally around or less than 3%. The lowest error was less than 1% under-prediction for the advance coefficient \(J=0.5\). Prediction of torque coefficient was not as successful because of the constant drag coefficient assumption. Grid independence was achieved for \(J=0.5\), 0.7, and 0.8. The CFD result was also validated for \(J=0.8\), i.e., the comparison between the converged CFD result and the experiment was more confident than the comparison between the CFD results themselves. In open water and behind-hull conditions, the unsteady phenomena and blade-to-blade effect occur only when the propeller wake field is very close to the propeller. This also supports the conclusion that the body force propeller model can be applied to many ship applications. For KP505 appended and operating behind the KCS hull in calm water, the thrust coefficient of the rotating blade model error was about 1%. For the downstream wake field, the rotating blade model provided a steady result closer to the experimental result than the average model's result. The high-velocity distribution was more scattered and had a lower value because the body forces were only distributed on the blades and the thrust was under-predicted. For the wake field right after the propeller, the unsteady phenomena were obvious. As the blades rotated into the fourth quadrant in sequence, the starboard area of high axial velocity appeared on the incoming blade and moved together with the blade until the blade left the quadrant. For the average model, the area of high axial velocity simply remained on the starboard side constantly and did not change over time. For E1619 in open water condition, the error was under-predicted by around 6%. The high-velocity areas behind each blade and velocity drops between the two blades are sufficiently captured by the rotating blade model. However, the area of lower velocity outside the propeller tip was not clear, because the grid number was not sufficient around the narrow blade tip. The contribution of the presented study is the implementation of the total velocity concept and blade rotation with 2D blade geometry in a CFD body force propeller model. Discretized real propeller simulation is still time consuming. Grid generation is difficult and complicated. The rotating blade body force model will be a great alternative for considering unsteady flow field phenomena and blade-to-blade effect. Only an additional cylinder disk is required. Grid generation is easy with a lower grid number. The same grid system can be applied for different propellers. In this study, it was also proven that the propeller model works in open water and behind-hull conditions. In future work, the propeller computation will be developed further to solve the vortex lattice on the grid cell found on propeller plane.