The new mixing length definition has been incorporated into the 



3 

 Douglas C-S boundary layer method of Wang and Huang. The original mixing 



length formulation is approximately valid and is used until the boundary 



layer thickness is greater than 20 percent of the body radius (6 >0.2 r_) . 



At this point, the boundary layer is considered thick and the mixing 



length £ is defined by 



/(r! 



2 2 

 ,+•5 ) -r^ 



^0 3.31 6 ^") 



Huang derived this equation and the limits on its use from the maximum 



13 

 values of mixing length given by Bradshaw, i^, and the experimental data 



of Huang et al. 



TURBULENCE REYNOLDS NUMBER 

 The axial turbulence velocity Reynolds number is defined as 



A 



,2 



h - -^ (^^) 



where \ is the microscale of the turbulence computed by the relationship 



,2 2 



u' u 



X^ = "" "" (18) 



du ^ 



Here, Taylor's hypothesis, the assumption of an isotropic field of turbu- 

 lence (although not quite true in Figure 10) and space-time equivalence, 



is used to obtain the microscale A. The time differentiation of u' was 



x 



accomplished by using an analog operational amplifier (as used by Frenkiel 



14 

 et al. ) in a differentiating mode. The departure from linearity as a 



42 



