134 



FIGURE 6. Computed and measured static pressure distributions across stern boundary layer of afterbody 2. 



indicating that the mean streamlines are concave. 

 Thus, the curvatures of the mean streamlines are 

 more closely related to the curvatures of the dis- 

 placement body than the actual body. The close 

 agreement between the computed and measured static 

 pressure distributions again supports the displace- 

 ment body concept for computing the potential flow 

 outside of the displacement surface. 



5. MEASURED AND COMPUTED MEAN VELOCITY PROFILE 



The incompressible steady continuity and momentum 

 equations for thin axisymmetric turbulent boundary 

 layers are 



8(rUg)/3s + 3(rVj^)/3n = 



(1) 



r^ is the body radius; x is the axial distance; u 



and Vj^ are the mean velocity components respectively 



parallel to and normal to the meridan of the body 



(s and n directions) ; v is the kinematic viscosity 



of the fluid; -u' V is the Reynolds stress; and u' 

 s n s 



and Vjlj are the velocity fluctuations in the s and n 



directions respectively. The Douglas CS method as- 

 sumes that the Reynolds stress depends upon the local 

 flow parameters only, e.g.. 



where 



for o < n < n 



for n < n < 6 

 c ~ 



(3) 



^o 



3u^ 



(eddy viscosity in the inner 

 region) 



and 



u 3u /3s + V 3u /3n 

 s s n s 



-dp/pds + 3[r(v3u /3n) -u' v' ] /r3n 

 s s n 



u (s,0) = v (s,0) = at n 

 s n 



(2) 



e = 0.0168 Y feu -u )dn = 0.0168 U 6* Y 

 o tr -'q e s e p tr. 



(eddy viscosity in the outer region) , 



^ m (^) 



A r 



o . 



0.4 r ln( ) S 1 - exp 

 o 



where 



r(s,n) = r (s,n) + n cosa 

 o 



a = tan"-''(dr /dx) 

 o 



(mixing-length parameter in the inner 

 region) , 



w — % 

 = 26 v( — ) , (Van Driest 's damping 



factor) , 



