180 



FIGURE 15. Criterion for separation. 



and theoretical studies may give a firmer founda- 

 tion for the present criterion. 



from the outer part where the flow does not differ 

 greatly from the unseparated flow. The newly- 

 generated vortex is confined to this region. 



Figure 17 is free-surface flow of MS-02. It 

 shows more clearly the existence of the above 

 mentioned, separated retarding region. The divid- 

 ing streamline can be observed which coincides with 

 the border line of the separated retarding region. 



In the case of practical ship forms, we have not 

 enough information as to whether or not such regions 

 exist. But from the velocity profiles of GBT-125 

 (Figure 14) , their existence can be supposed in 

 those cases also. 



According to the present experimental studies, 

 it is implied that any single approximate equation 

 of the Navier-Stokes equation completely governs 

 the flow field near the stern. 



Eddy Viscosity Coefficient in Wake 



In order to predict turbulent terms in the Navier- 

 Stokes equation, there is a concept of eddy viscos- 

 ity. It is based on an idea that momentum loss due 

 to turbulence can be represented by momentum loss 

 due to friction and the coefficient is constant as 

 to positions and directions. According to this 

 assumption, the Navier-Stokes equation is written. 



q. Vto 



j.Vq 



V v^u 



(27) 



Flow Field after Occurrence of Separation 



Once separation has occurred, the flow fi'eld differs 

 greatly from the unseparated boundary layer flow. 

 The existence of the dead region, pointed out in 

 the previous section, is one phenomena. 



Figure 16 shows velocity profiles, after the 

 occurrence of separation, measured by the hot film 

 anemometer. The bars in the figure represent fluc- 

 tuations in velocity. The region where the velocity 

 fluctuates so intensively and is very low consists 

 of a characteristic thin layer, a separated retard- 

 ing region. It can be definitely distinguished 



where v is the eddy viscosity coefficient. 



Equation (27) is a kind of diffusion equation 

 with Vg the diffusivity coefficient. It can be 

 determined ejcperimentally ; substituting the measured 

 values of velocity and vorticity into Eq. (27) 

 leaves only v^ as an unknown. 



Using experimental data of the GBT-30, covering 



1.08<x<1.16, Ve is determined by the least-square 



method. The estimated values of v„ are not unique; 



_i, 

 they differ slightly for each direction, 2.7 x 10 , 



2.4 



10" 



and 1 . 6 



10" 



for co^ 



and CD„ 



The 



mean value is 2.2 x 10" , and consequently the 

 equivalent Reynolds number, based on the eddy vis- 

 cosity, is about- 1/300 of the real Reynolds number. 



100 



(mm) 



50 



FIGURE 16. Velocity profiles 

 near the separation position 

 (MS-02) . 



INTENSIVE 

 FLUCTUATION 



S.S. ^ 



50 



: 

 t 



s.s. 



50 



S.S. T 



50 





' 8 # S.S. ^ 



50 





/ - 



Z=-0.02 



Mi, 



0.3 



0.3 



0.3 



0.3 



0.5 



