178 



P((l»9''«) 



F.P. 9 8 7 6 5 4 3 2 

 FIGURE 12. Comparisons of crossflow angle (GBT-125). 



just behind the bilge keel and the occurrence of 

 bilge separation can be suspected. 



Shape factor H, in every case, does not vary 

 significantly and agreements between calculations 

 and measurements are good except near the stern. 

 There, as shown in comparisons of 6, large cross- 

 flow angles existed and the present scheme can not 

 be employed here. 



It is interesting that large crossflow angles 

 can also be observed in experiments near the bow. 

 They create a suspicion of the occurrence of bow- 

 bilge separation. 



Skin friction t^, shows also good agreement. 

 It is observed that both experimental and calculated 

 values do not decrease. This suggests three- 

 dimensional separation differs a little from that 

 of two-dimensional where skin frictions vanish. 



As a whole, it can be safely concluded that, 

 except near the stern, calculated results show good 

 agreements with measured as far as integral quanti- 

 ties like 9ii or H. It can be also concluded that 

 the present scheme, using integrated mementum bound- 

 ary layer equations as governing equations , can be 

 appreciated in spite of its brevity. 



EXPERIMENTAL STUDIES ON BOUNDARY LAYER SEPARATION 

 AND WAKE 



Kinds of Ejcperiments and Measuring Techniques 



The characteristics of separation and separated 

 flow of ship-like bodies are dim. Experiments may 

 throw light upon them. In order to discuss the 

 characteristics of separation and separated flow, 

 the following experiments were carried out in addi- 

 tion to the previous experiments. All experiments 

 were carried out with MS-02 and experiments (c) and 

 (d) used GET- 30 also. Experiments were executed 

 at the speeds of Fn=0. 1525 (Rg=2. 17x10^) and Fn=0 . 16 

 (Rg=2. 38X10^) for MS-20 and GBT-30 respectively. 



Flow Observations 



Planting twin tufts on the hull surface, flow di- 

 rections near the stern were observed by a submerged 



camera; one tuft was just on hull surface and the 

 other was 22mm off, normal from surface. 



Free-surface flow around the ship stern was also 

 observed in relation to the separated flow by the 

 aluminium powder method. 



Velocity Measurements in Separated Flow Region 



Velocity in the separated region was measured using 

 a hot film anemometer. The probe is a conical type, 

 2mm in diameter. One horizontal plane of z=-0.02 

 was covered where framelines are almost vertical. 

 Because the probe was set parallel to the uniform 

 flow, the velocity is not quantitatively accurate. 



Velocity Measurements in Wake 



Two five-hole pitot tubes were used for velocity 

 measurements in the wake; 8mm-diameter tube for MS-02 

 and lOmm-diameter tube for GBT-30. For estimations 

 of vorticity, measurements were carried out on three- 

 dimensional lattice-points spaced 0.025, 0.015, and 

 0.015 in X, y, and z directions respectively. 



Vorticity Estimations in Wake 



The vorticity can be estimated by differentiating 

 the measured velocity distributions; 



8w 



3y 



_8v 

 3z 



3z 



3w 

 3x 



3v 

 3x 



_3u 

 3y . 



(25) 



The differentials were obtained numerically by 

 three-point approximation. 



Discussions on Boundary Layer Separation and Wake 

 Flow 



Boundary Layer Flow near Separation 



Figure 13 shows flow directions near the stern of 

 MS-02 obtained by the twin tufts method. 



It was observed that, very near A. P., both tufts 

 are drooping. This means that the velocity is al- 

 most dead; in other words, separation has occurred. 



On the remaining parts, the outer tufts show 

 almost the same direction as the calculated poten- 

 tial flow direction; on the other hand the inner 

 tufts differ greatly from them and produce large 

 crossflow angles. A reference to the surface pres- 

 sure distribution gives a clear explanation that 

 flow near the hull surface, whose velocity is very 

 low, cannot make further steps against the pressure 

 increments and change direction suddenly from the 

 external streamwise direction toward the low- 

 pressure regions. Significant occurrences of shear 

 flow and generation of vortices are assumed which 

 correspond to beginnings of three-dimensional sepa- 

 ration. 



The above situation can be understood more 

 clearly from velocity profiles in the boundary layer 

 near separation. Figure 14 shows the velocity pro- 

 files of GBT-125 along streamline Nos. 5, 9, and 

 11. A sudden large crossflow occurs near S.S.^j 

 for all the streamlines and, correspondingly, the 

 streamwise velocity profile also changes. The 



