217 



(SqSt.-^.PORT) 

 -8 -6 -4 -2 



(Sq.Sl.-i-, 



STARBOARD) 



2 4 6 8 

 Z.Y=I = 35rT»n KS.NqM-V 

 = 20 mm M.S.N QM-^ 



FIGURE 21. Cross section of vorticity distribution 

 (M.No.M-7 and M-4 , Sq.St. 1/8). 



FIGURE 22. Cross section of vorticity distribution 

 (M.No.M-7, at Sq.St. 1/2 and 1/4). 



of the vortex sheet are fairly similar for both 

 geosim models. On the other hand, the difference 

 in breadth of each model ' s vortex core seems to be 

 due to the effect of difference in Reynolds number. 



Furthermore, the suitability of adopting the 

 idea of the Max. line is shown by the following 

 facts. Assuming that all the vorticity of the 

 stern vortices are concentrated on the Max. line 

 for computing the induced velocities, the resul- 

 tant velocity vector diagrams are similar to the 

 complete flow field velocity. For instance, 

 Figure 23 is a diagram of velocity vectors, which 

 have the same circulation value as Figure 8 but 

 with the vorticity concentrated on the Max. line 

 divided by ten, of circular vortices with mean 

 strength on the original Max. line. It can be 

 seen that both diagrams of the velocity vector. 

 Figure 10 and Figure 23, are fairly similar. This 

 will allow not only simplified treatment of the 

 stern vortices but also should simplify future 

 numerical analysis of the stern vortices. 



In order to predict the wake of full stern 

 ships, it is necessary to estimate the wake com- 

 ponent due to the stern vortices in addition to 

 the potential and frictional wake components used 

 in Sasajima's wake prediction method. The concept 

 of the Max. line in the vorticity distribution 

 also may lead to the wake component due to the 

 stern vortices. 



In order to discuss the relation between the 

 stern vortices and the wake distribution, an 

 illustrative model of the stern vortices is 

 presented in Figure 24. A stream line flowing 

 under the bottom of a ship, separates around the 

 bilge and forms a part of the separating vortex 

 sheet. The vortex sheet crosses to the hull 

 surface near the propeller bossing where the 

 authors denote the secondary separation line. 

 And at the secondary separation line, the vortex 



sheet makes the cross flow with the limiting stream 

 line flowing aft passing through the tunnel of 

 the vortex sheet. The crossed flow generates a 

 reversed vortex at the secondary separation line 

 as seen in the diagrams of the vorticity distribu- 

 tion. 



The flow passing through the tunnel of the 

 vortex sheet can be found at the section of the 

 propeller disk (sq.st. 1/8) which appears as an 

 eye in the wake distribution pattern in Figures 17 

 and 18. This fact may be proved by the Max. line 

 which just covers the eye. 



8 10 



FIGURE 23. Velocity vectors due to concentrated vor- 

 ticity on max. line (M.No.M-7, Sq.St. 1/8). 



