TURBULENCE MODEL 



Figure 12 shows that the distribution of measured mixing length in 



the thin boundary layer is roughly approximated by the thin boundary layer 



13 

 results of Bradshaw et al. However, the thick boundary layer values of 



il/6 are considerably smaller than Bradshaw' s thin boundary layer results. 



Figure 12 also shows that the maximum values of the mixing length occur at 



approximately the same radial location for theory and experiment. Huang 



et al. proposed that the mixing length of an axisymmetric turbulent 



boundary layer is proportional to the square root of the entire turbulence 



annulus between the body surface and the edge of the boundary layer 



£ ~ /(r +6 )2-r2 



(15) 



'/^ 



2 2 

 The present measured values of £/V (r„+6 ) -r_ are given in Figure 13 



r .. ^ 



where the solid curve is derived by Huang et al. This figure shows that 

 the values measured agree reasonably well with Huang's hypothesis. 



V 



- 













X 



L 

 O 0.704 



D 0.831 





'£ 



• 









O 0.873 



- 











A 0.909 





^^^ 





s 



• 





A 0.951 



- 



<<^:>—~^^ 



D 







• 0.987 





Dc^ O 



A. 



^ 









'•A^ 



ik 







\ 



\^ 





■*# 











\ 





Ih 











A \ 



\<> 



'i^ 1 



1 1 





1 





1 



\ 



0.0 0.2 



0.4 0.6 0.8 1.0 1.2 1.4 



Figure 13 - Similarity Concept for Mixing Length of Thick 

 Axisymmetric Stern Turbulent Boundary Layer 



41 



