138 



MEASUREMENT 



(Al 0-840 <J (^ 0.962 



IBI 0.934 <^ Q 0.484 Q 



(C) 0.970 A ^ 0.206 



(Dl 0.977 □ O 0.149 Q 



I-'IC;URL-; 10. Measured and computed mean axial and radial velocity distributions across stern boundary 

 layer of afterbody 2. 



layer by means of the displacement body concept. 

 However, it is important to point out that the 

 measured axial velocity profiles in the inner region 

 are in general smaller than the theoretical values. 

 The eddy viscosity model plays an important role in 

 this region; therefore, it is essential to examine 

 the eddy viscosity model used for computing the 

 thick stern boundary layer. Figures 8 and 10 also 

 show the comparison of the axial velocities mea- 

 sured by the cross-wire and by LDV (Huang et al., 

 1976) . The agreement is very good inside the bound- 

 ary layer. However, due to the artifical seeding 

 of oil mist required for the LDV, the axial veloc- 

 ities near the edge of the boundary layer measured 

 by LDV are smaller than that by the cross-wire. 



6. 



COMPARISON OF MEASURED AND COMPUTED INTEGRAL 

 PARAMETERS 



Ujj(r) is computed by the potential-flow method ex- 

 cept inside of the displacement surface where it is 

 assiomed that U (r) = U (r^) with r, being the radius 

 of the displacement surface. The boundary-layer 

 thickness S^ is defined at the radial position where 

 the measured value of Ux*'^' equals 0.995 Ux(r). It 



is difficult to obtain 



precisely since the ac- 



curacy of the Uj,/U measurement is only about 0.005. 

 Nevertheless, the overall accuracy of the values of 

 6j- estimated in the present investigation is about 

 10 percent. 



A measure of the mass-flux deficit in the thick 

 axisymmetric boundary layer is defined by 



r +6 

 /^o r 



A = 



u (r) 

 x 



U (r) 



r +6* 

 _o r 



rdr 



rdr 



(11) 



The integral parameters are derived from the mea- 

 sured velocity distribution. The two-dimensional 

 displacement thickness is defined as 



where r is the local body radius and 6* is the 

 axisymmetric displacement thickness. Thus, the 

 axisymmetric displacement thickness becomes 



/ 



1 - 



u (r) 



X 



U (r) 



dr 



(10) 



where 6j, is the boundary thickness measured radially 

 normal to the body axis and Uy.{r) is the value of 

 the axial component of inviscid flow velocity com- 

 puted about the displacement body. The value of 



r + 6* 

 o r 



+ 2 



^ 2 

 max 



(12) 



where r„ 



is the maximum radius of the body. 



The displacement body in the present investiga- 

 tion is defined by r^ = 6^ + r^ rather than the 



planar definition, r^ 



*i 



Similarily, a 



measure of the momentum- flux deficit is defined by 



