204 



INPUT SHIP FORM 



INTERPOLATION BY CUBIC SPLINE FUNCTION 



FIGURE 20. Body plan for ship model 5 350. 



both sides of the corner region and, hence, enhances 

 the thickening of the boundary layer. This thicken- 

 ing of the boundary layer in the corner region of 

 ship hulls has been verified experimentally by Hoff- 

 mann (1976) . 



6. CONCLUDING REMARKS AND FUTURE WORK " 



According to the studies presented in this paper, 

 the three-dimensional boundary layers on ship hulls 

 can be computed very efficiently and effectively. 

 The turbulence model, as in two-dimensional flows, 

 again yields satisfactory results for three- 

 dimensional flows. This has been demonstrated 

 by Soejima and Yamazaki (1978) who also have applied 

 the present turbulence model to compute three- 

 dimensional boundary layers on ship hulls. However, 

 there are additional studies and problem areas that 

 need to be considered and investigated before the 

 present method can become a more effective tool to 

 design ships. They are briefly discussed below. 



Generation of Initial Conditions on Arbitrary 

 Bow Configurations 



In Section 5, we presented calculations for the ship 

 model 5350 and mentioned that due to flow separation 

 in the bow region, we had to start the boundary-layer 

 calculations at some distance away from the bow. 

 Additional studies are required to generate the ini- 

 tial conditions on the bow. These studies can lead 

 to a better design of bow configurations and to 

 better handling of bilge vortices, which contribute 

 to the total drag of the ship. However, this is by 

 no means an easy task. Consider, for example, the 

 ship model 5350 discussed earlier. A sketch of the 

 bulbous nose with a plausible inviscid streamline 

 distribution is shown in Figure 26. We assume 

 that the ship is symmetrical about the keel plane 

 and there is a nodal attachment point on the bulbous 

 nose at B. If the ship is floating, then the water 

 line is determined by conditions of constant pressure 

 and zero normal velocity. Hence the intersection A 

 of the plane of symmetry with the water line and the 



FIGURE 21. Pressure distribution 

 for the entire ship model 5350. 



