200 



FIGURE 12. Comparison of com- 

 puted total velocity profiles 

 with Vermeulen's data. 



factor, Hji, the Reynolds number based on the momen- 

 tum thickness, Rg , and the limiting crossflow angle 

 for x/L = -0.85, 0.0, and 0.75. As can be seen from 

 these figtures, the boundary- layer parameters vary 

 greatly near the keel where the curvatures and the 

 pressure gradients are large and remain almost un- 

 changed near the surface where the curvatures and 

 the pressure gradients are small. Except at x/L = 

 -0.85, the limiting crossflow angle is positive. 

 This implies that the crossflow near the wall moves 

 from the keel to the free surface as predicted from 

 the pressure distribution. Figure 17 shows typical 

 longitudinal and transverse velocity profiles at 

 2=0.6 for several values of (x/l) , and Figure 18 

 shows typical transverse velocity profiles at (x/L) 

 = -0.2 for several values of z. As can be seen from 

 Figures 17(b) and 18, the transverse velocity compo- 

 nent undergoes drastic changes in the longitudinal 

 and transverse directions under the influence of 

 pressure gradient and body geometry. As was dis- 

 cussed before, when the transverse velocity changes 



sign across the boundary layer and contains regions 

 of reverse flow, numerical instabilities results from 

 integration opposed to flow direction unless appro- 

 priate changes are made in the integration procedure. 

 The new numerical procedure of Cebeci and Stewartson 

 (1977) handles this situation very well and does not 

 show any signs of breakdown resulting from flow re- 

 versal of transverse velocity component. 



Results for Ship Model 5350 



The ship model 5350, 

 previous section, is 

 geometry of the hull 

 represented in tabula 

 The model possesses a 

 existing merchant and 

 bottom which is flat 

 water surface and an 

 merged under the wate 



unlike the one discussed in the 

 a realistic tanker model. The 

 is so complicated that it is 

 r form section by section. 

 11 the special features of 

 naval vessels, that is, a 

 and not parallel to the still- 

 extended bow completely sub- 

 r surface, and consequently 



