137 



Cp(r), across the thick boundary layer is expressed 

 in terms o f the inv iscid resultant velocity Up 

 [Up(r) = /l - Cp(r) ] and 9 is the angle between the 

 inviscid resultant velocity Up and body axis (6 is 

 positive when Up is directed away from the axis) . 

 In the first improvement the values Us/(UpCos (S-a) ) 



are taken as the computed values of f 



Us/Up 



the CS method with Ug equal to the inviscid resul- 

 tant velocity on the displacement body. At the edge 

 boundary layer, the value of Ug (UpCos (9-a) ) is equal 

 to 1.0. The value of Vj^/(U sin( 9-a) ) is also equal 

 to 1.0 since the boundary-layer-induced normal ve- 

 locity is assumed to be equal to the inviscid normal 

 velocity of the displacement body at that point 

 [Lighthill (1958) ] . The theoretical proof for an 

 axisymmetric body has not been worked out in the 

 literature and will not be given here. However, 

 the validity of the assumption will be borne out 

 by the experimental measurements of v . Therefore, 

 Eqs. (6) and (7) reduce to the proper limit at the 

 edge of the boundary layer, e.g.. 



u (r=6 ) 

 X r 



V (r=6 ) 

 r r 



(8) 



(9) 



which are the inviscid axial and radial velocity 

 components of the displacement body, where Or = 



A - C (r = 6 ) . Outside of the boundary layer, 

 Eqs. (8) and (9) are also valid so long as the 

 local inviscid values of Up and 9 for the displace- 

 ment body are used. The improved values in Eqs. 

 (6) and (7) account for the variation of the in- 

 viscid static pressure and potential-flow vector 

 across the thick boundary layer and make appropriate 

 use of the results of the CS method. As already 

 noted, the variation of static pressure computed 

 across the boundary layer outside of the displace- 

 ment surface agrees quite well with the experimental 

 results. 



Figure 8 shows the comparison of the mean axial 

 and radial velocity profiles at several axial sta- 

 tions on Afterbody 1, and Figure 9 shows the mea- 

 sured axial velocity profiles across the near wake 

 of Afterbody 1. The theoretical results at X/L = 

 1.00 were calculated at X/L = 0.998. Figures 10 

 and 11 show comparisons of the measured and computed 

 velocity profiles for Afterbody 2. The mean axial 

 and radial velocity components u^ and Vj. were mea- 

 sured by a cross-wire probe and the experimental 

 accuracy of measurements of u^^/Uq and Vj-/Uq were 

 respectively about 0.5 percent and 1.0 percent. 



As shown in Figures 8 and 10, the theoretically 

 computed velocities , which account for the variation 

 of static pressure distribution across the thick 

 boundary layer, agree better with the measured axial 

 and radial profiles outside of the displacement sur- 

 face. These results suggest that a simple improve- 

 ment of the existing boundary-layer computation 

 method can be made for the thick stern boundary 



1.4 



1.2 



1.0 



0.8 



0.6 



0.4 



0.2 



0.2 



0.4 



0.6 



0.8 



1.0 



FIGURE 9. Measured mean axial velocity distributions 

 across near wake of afterbody 1 . 



