179 



S.S.I 



FIGURE 13. Flow directions near 

 stern and isobar lines (MS-02) . 



STWWllKE WO. 9 



Ll^ 





i 



'I 



0.2 0.2 



STREAHINE 

 . NO. 9 



31. 



5'"""> STREftHltiE H0.5 | * , .* 5.S.I.* J. .* ' .* / • ^ ? •* < .* 



1 r~/ i: ^.' •• / / ..• i ! 



ss,/ V / ; / / : .••• ; / / / 



/ ' / / .^^ .-.>^ . -■,...•< ^ q "■'' <'•« "■' "■'' '■" 



^^r ^ _^ ^ y ^, q. 0.6 0.4 0.4 0.4 Ue 



0.4 0.4 0.4 0.4 U« 



FIGURE 14. Velocity pro- 

 files in boundary layer 

 near the stern (GBT-125) . 



maximum crossflow velocity amounts to about half 

 of the streamwise velocity. 



Such behaviors of flow near the stern are not in 

 the category of boundary layer flow, therefore, 

 boundary layer calculations should be stopped and 

 another treatment employed. 



Criterion for Boundary Layer Separation 



It is necessary to introduce some criterion for 

 boundary layer separation in order to change the 

 governing equations from boundary layer to some 

 others . 



There are many criteria mainly for two-dimensional 

 separation [e.g., Chang (1970)]. 



A parameter, r^, defined by 



^a = -\jf T^ ' (26) 



wl 



is proposed. 



The proposal is based on the experimental facts 

 that the beginning of three-dimensional boundary 

 layer separation is closely related to the pressure 

 gradients, as discussed in the previous section, 

 and that boundary layer flow, such as with large 

 momentum thickness and small skin friction, can no 

 longer exist. Therefore, flows with large values 

 of r^ cannot exist in real flow in the sense of 

 boundary layer flow. On the other hand, if the 

 boundary layer assumptions are kept, the calculated 

 values of r^ can increase without any upper bound. 



Figure 15 shows V^ obtained by the boundary 

 layer calculations and from experiments. The calcu- 

 lated values get increasingly large approaching 

 the stern, but experimental values do not and they 

 seem to have some upper bound. 



The value of T^ = 20 is reasonable as a criterion 

 for separation, because, as shown in Figure 14, 

 large crossflow angles were observed near x=0.9 

 (S.S.Sj) and the onset of separation is suspected. 



Of course , more experimental data are necessary 

 for the present discussion and further experimental 



