203 



20 30 40 50 60 70 80_g,5 



rjl = (u./^s,l"^¥> 



-0.10 -0.05 



0.15 



FIGURE 17. Computed longitudinal and transverse velocity profiles for the double-elliptic ship model for R^ 

 10^ at z = 0.6. 



is favorable and then later becomes adverse. The 

 pressure gradient in the transverse direction de- 

 creases rapidly from the keel to a minimum value 

 and then increases continuously up to the free sur- 

 face. Due to this rapid pressure variation in the 

 bow region, preliminary boundary-layer calculations 

 showed flow separation and required an approximate 

 procedure to generate the solutions for x < 22.5 m. 

 After that (x > 22.5), the three-dimensional boundary- 



-0.03 -0.02 -0.01 



FIGURE 18. Computed transverse velocity profiles. 



layer calculations were performed for a given invis- 

 cid pressure distribution. The initial conditions 

 at X = 22.5 m were generated by solving the boundary- 

 layer equations in which the z-wise derivatives for 

 a constant z were neglected. 



Figures 23 to 25 show some of the computed re- 

 sults for R^ = 3 X 108 . Figure 23 shows the varia- 

 tion of Cp, cf, Rg , Hj J , and 6^^ at the cross-planes 

 of X = 30 m, 105 m, and 210 m. Typical streamwise 

 velocity profiles at x = 105 m and z = 0.2 are shown 

 in Figure 24 and typical crossflow velocity profiles 

 at x = 60 m are shown in Figure 25. As can be seen 

 from these figures, the crossflow velocity profiles 

 show great variations and indicate clearly the flow 

 reversal that takes place in the crossflow plane. 

 This implies that differential methods based on two- 

 dimensional and/or small crossflow approximations as 

 well as methods based on integral methods are not 

 adequate to boundary-layer calculations on ship 

 hulls. Other interesting results that emerge from 

 these calculations are the sudden jumps of the limit- 

 ing crossflow angle from positive to negative, and 

 the thickening of the boundary layer in the corner 

 region of the crossplanes. The jumps of the cross- 

 flow angle indicates the convergence of the flow from 



FIGURE 19. Three-dimensional view of ship model 5350 

 with the nonorthogonal coordinate system. 



