axes. A new mixing length model is assumed to apply to a thick three-dimensional 



stern boundary layer. The schematic representation of effective turbulence areas, 



as determined by the areas between the body surfaces and the contours of 0.66 at 



x/L =0.81 and 0.95, are shown in Figure 17. The out side edges of the effective 



/ ^ 

 turbulence areas are very close to the contours of «/ ^^ /U =0.04. Further out- 



^ T X o 



side of these edges, turbulence intensities reduce to 0.01 at the edge of the 

 boundary layer. The mixing length parameter is assumed to be proportional to the 

 square-root of these effective turbulence areas, e.g.. 



£ ^ v/(a+0.66 )(b+0.6S^)-ab = A(x) 

 a b 



where the value of e is assumed to be small and will be neglected and the value of 

 a 



e, is zero since no separation occurs there. The values of e and £, may not be 



negligible if the separation region is so large that the effective turbulence area 



is reduced significantly. However, in the inner region, the conventional mixing 



length in the wall region. Equation (2), is assumed to apply. The mixing length % 



is assumed to be the same at the intersection of the inner and the outer region, 



y = y in Equation (2) . Figures 18a through 18c show the normalized mixing length 



c Y 2 



distributions for three axisymmetric bodies studied by Huang et al. ' These figures 



show that the measured values for the three axisymmetric models agree reasonably 

 well; each peaking at a value of approximately 0.05. The values of Ilk at various 

 locations for the present three-dimensional model are shown in Figures 18d through 

 18j. With the exception of the 80-degree angular location, values of the non- 

 dimensional mixing length remain fairly constant over the stern with respect to both 

 angular and axial positions. 



The data in Figure 18 support the use of a revised mixing length formulation. 

 The existing thin turbulent boundary- layer method can be applied to the axisymmetric 

 or three-dimensional elliptical body at locations forward of where the boundary 

 layer thickness reaches 20 percent of the major or minor axis value. Downstream of 



this location, the apparent mixing length £ may be approximated by the thin flat 



13 

 boundary layer of Bradshaw et al. as 



17 



