198 



FIGURE 7. Comparison of gener- 

 ated initial total velocity 

 profiles with Vermeulen's data. 



GENERATED PROFILES 

 DATA 



Se 



tang 



(68) 



with the limiting crossflow angle g„ obtained from 

 the experimental data. 



Once the streamwise and crossflow velocity pro- 

 files are calculated by the above procedure , we 

 compute the velocity prof: les u/u^ and w/Wg in the 

 orthogonal directions x and z by the following rela- 

 tionships 



u u w 

 ^ = -^ - ^ ^ (69a) 



"e "se "se "e 



^ = ^ + ^ ^ {69b) 



W= Uo U„ W„ 



e ^e ^e e 



Figure 7 shows a comparison of generated and 

 experimental total velocity profiles along the line 

 A. As can be seen, the procedure discussed above 

 for generating the initial velocity profiles from 

 the experimental data is quite good. This is impor- 

 tant for an accurate evaluation of a turbulent 

 model, especially for three-dimensional flows. 

 Here 



(70) 



The solution of the boundary-layer equations also 

 requires the specification of the metric coefficients 

 and the geodesic curvatures. They are calculated 

 from the following expression: 



hi = 



h2 = 1.0, 



Ki = 



straight section 



z/R curved section 

 ' o 



K2 = 



straight section 



1/(R -z) curved section 



(71) 



A comparison of calculated and experimental values 

 of streamwise momentum thickness, 6jj, shape factor, 

 Hu, skin-friction coefficient, Cf, and limiting 

 crossflow angle, Svj, is shown in Figures 8, 9, 10, 

 and 11, respectively, along the lines B, C, D, E. 

 Here the limiting crossflow angle is computed from 



PRESENT METHOD 

 E 



FIGURE 8. Comparison of computed momentum thickness 

 with Vermeulen's data. 



FIGURE 9. Comparison of computed shape factor with 

 Vermeulen's data. 



