A spline curve is used to fair the experimental data before the velocity gradient 

 is obtained numerically. 



The nondimensional distributions of the eddy viscosity e/ (U ^6 *) determined 

 from the data are shown in Figures 15a through 15d. The parameters U;. and 6 * are 

 defined as the potential flow velocity at the edge of the boundary layer and the 

 planar displacement thickness, respectively, for the displacement body. The solid 

 curve she 

 given by 



curve shown in these figures is the Cebeci and Smith thin boundary layer formula, 



^P 1 + 5.5^^ 



0.0168 (3^ 



r 



All values of eddy viscosity for the 3:1 elliptic model are smaller than the experi- 

 mentally-derived values recommended by Cebeci and Smith for thin boundary layers. 



The experimentally-determined distributions of the nondimensional mixing length, 



£ /6 , are shown in Figures 16a through 16d. The solid curve in these figures 



P ^ 13 



represents the thin boundary-layer model of Bradshaw et al . Agreement between 



theory and measurements is, at best, fair for angular locations of and 67 degrees; 



for angular locations greater than 67 degrees, the measured values of mixing length 



are much smaller than the predictions. 



1 2 

 For an axisjmmietric turbulent boundary layer, Huang et al. ' proposed a 



turbulence model relating the mixing length to the square root of the entire tur- 

 bulence annulus area between the body surface and the edge of the boundary layer. 

 As seen in Figures 14 through 16, the values of measured turbulence intensity, eddy 

 viscosity, and intermittency across a turbulent boundary layer decrease from a 

 maximum value at 60 percent of the boundary- layer thickness to zero at the outside 

 edge of the boundary layer. The effective gross turbulence area relevant to the 

 mixing length parameter is [(a+0.66 ) (b+0. 66 )-(a+e )(b+e, )]; where e and e are 

 the effective thicknesses of the separation bubble (low turbulence mixing) in the 

 direction of the major and minor axes, a and b, respectively, of the elliptical 

 cross-section, and 6 and 6 are the boundary-layer thicknesses along the a and b 



16 



