218 



*^l/6 



SEPARATING 

 ; FLOW 



/limiting 

 - / stream line 



SECONDARY 



-SEPARATION LINE 



SEPARATION LINE 

 FIGURE 24. Illustrative model of stern vortices. 



This tunnel vortex sheet is quite different from 

 the conical vortex sheet used in the model proposed 

 by Sasajima or Hoekstra. Considering the flow as 

 passing through this tunnel makes it possible to 

 discuss the relationships of the wake flow, limit- 

 ing stream line, attachment line, and the stern 

 vortices. 



Regarding the wake patterns of vessel with a 

 full stern, the authors suppose that if the Max. 

 line can be considered independent of the Reynolds 

 number, then the "eye" in the ship's wake pattern 

 should be in approximately same location as shown 

 in Figures 17 and 18. The above mentioned facts 

 will lead to further studies for prediction of 

 ship's wake, using the potential and frictional 

 wake patterns estimated by Sasajima 's method. 



Actually, the authors cannot verify the 

 relationship between the stern vortices and 

 Reynolds number because the range of the scale 

 ratio used in geosim models tested is too small 

 for a discussion of the similarity of the stern 

 vortices. However, it can be said that the 

 alternation of the Max. line between both models 

 seems relatively smaller than that of the wake 

 pattern. Furthermore, the vortex center, which is 

 defined as the vanishing point of the induced 

 velocity vector due to the stern vortices, has 

 shifted a distance corresponding to only 4% of the 

 propeller diameter as seen in comparing Figures 10 

 and 11. While the model size has comparatively 



FIGURE 25. Relation between vorticity and velocity 

 of model ship. 



small effect on the shape of the Max. line, the 

 model size causes differences in the diffusion of 

 the vorticity. Thus, from the calculation of the 

 circulation of the vortex cores presented in 

 Figures 8 and 9, it was found that the circulation 

 of M.No.M-4 was smaller than M.No.N-7. The magni- 

 tudes of these differences were 6% smaller on the 

 portside and 8% smaller on the starboard side of 

 M. No. M-7. However, even for the same model ship, 

 the difference in the port and starboard side 

 stern vortex circulation was on the order of 8%, 

 so it is not possible to reach a definite conclu- 

 sion about the significance of the differences in 

 the geosim tests. 



Since the authors limited study to vessel speeds 

 corresponding to Froude number 0.18, the effects 

 on the velocity due to the stern vortices still 

 remains obscure. However, the authors can in- 

 dicate some examples in which the vorticity has 

 been measured at the several mesh points as seen 

 in Figure 25. If the free surface effect could be 

 neglected, the non-dimensional vorticity Cx should 

 be constant. Although the cause of the different 

 results explicitly shown in Figure 25 remains un- 

 known, it may not be said that the rotor-shaft 

 friction of the vortexmeter can be safely considered 

 as negligible in a range of very slow speeds such 



as F < 0.1. 

 n 



Q6 



FIGURE 26. Circumferential distribution of 

 wake flow on propeller disk, Vj(/U. 



O 0.6 - ' 



Bolton 



9 (dcg.) 



