## 3 Results
### KP505 Propeller in Open Water Test
#### 3.1.4 Propeller Wake Field  
Figure 10 shows the velocity profile behind the propeller for \(J=0.8\). The flooded contour is the axial velocity, and the vector field includes both lateral and vertical velocities. For the rotating blade model, the blade-to-blade effect to the flow field is clearly observed at x/\(L=0.005\) (Figure 10a). In the radial direction, the high-velocity region is located around \(r/R=0.4\) to \(0.8\). It is not axisymmetric along the circumferential direction. The velocity drops slightly between two adjacent blades, i.e., the trailing edge of the current blade and the leading edge of the next blade. The area shrinks as well. The flood contour near the blade leading edge has a clear concave shape. However, at just slightly downstream (e.g., \(x/L=0.01\) in Figure 10b) the flow field of rotating blade model becomes almost axisymmetric. The contour pattern is almost identical to the average model one in Figure 10c, which is steady, i.e., it would not change by time.  
Figure 9: Body force distribution on the propeller plane (\(J=0.8\)): (**a**) rotating blade model; (**b**) average model.  
In Figure 11 (\(J=0.8\)) and Figure 12 (\(J=0.6\)), the free surface waves caused by the propeller excitement have a very small amplitude, because the propeller immersion depth is in deep water. In the comparison of both propeller models, the wave amplitude of the rotating blade model at a specific timepoint is smaller than that of the average model at the same timepoint. It decays more obviously and faster in the far downstream region as well. This phenomenon is more obvious for \(J=0.6\), and the waves become more laterally scattered downstream in the rotating blade model. This is because the body forces are only distributed on the blades, producing discontinuous influence in the lateral direction on the free surface. Comparing the different \(J\) values, the lower \(J\) shows a higher axial velocity on the propeller plane, a larger wave amplitude, and a shorter effective pitch indicated by the streamlines.  
Figure 10: Propeller wake flow field: (**a**) rotating blade model (on \(x/L=0.005\) plane behind the propeller); (**b**) rotating blade model (on \(x/L=0.01\) plane behind the propeller); (**c**) average model (on \(x/L=0.005\) plane behind the propeller). Here, \(x/L=0\) is at the propeller center.  
Figure 13 plots the 3D vorticity lines to observe the vortex shedding behind the propeller KP505. The propeller rotational flow with (high frequency) tip vortex shedding is clear in the figure. Additionally, on the propeller plane each blade tip corresponds with a lower velocity area outside the propeller radius.  
Figure 11: Free surface elevation and streamline (\(J=0.8\)): (**a**) rotating blade model; (**b**) average model. (The \(u/U\) distribution is the slice at propeller plane \(x/L=0\) and the undisturbed free surface is at \(z/L=0\)).  
Figure 12: Free surface elevation and streamline (\(J=0.6\)): (**a**) rotating blade model; (**b**) average model. (The \(u/U\) distribution is the slice at propeller plane \(x/L=0\) and the undisturbed free surface is at \(z/L=0\)).