I 1 for 6 < 0.2a and 6^ < 0.2b 



X. a — b — 



o 



/[a(x)+0. 66 (x) ] [b (x)+0. 66, (x) ]-a (x)b (x) 



X, a b 



(9) 



o /[a(x^H0.66^(x^)][b(x^H0.66^(x^)]-a(x^)b(x^) ^^ \ ^^^b 



for 6^ > 0.2a 

 b 



where x is the axial location downstream of the initial location of the thick stern 



boundary layer x . The beginning of the thick stern boundary layer is selected as 

 in 



the axial location where the local value of 6 or 6, grows to the value of 0.2a or 



a b 



0.2b, respectively (whichever occurs first). The new formulation can be incorporated 

 into existing axisymmetric and three-dimensional turbulent boundary-layer differ- 

 ential methods and must be evaluated for a variety of stern boundary layers before 

 its validity can be fully established. 



CONCLUSIONS 



The results of recent experimental investigations of the thick stern boundary 

 layer on a three-dimensional body having 3:1 elliptic transverse cross sections are 

 presented. Comprehensive boundary layer measurements, including mean and turbulence 

 velocity profiles and static pressure distributions are given in detail. 



An initial attempt has been made at extending to three dimensions the Lighthill 

 and Preston displacement body concept used to treat the viscid-inviscid stern flow 

 interaction on axisymmetric bodies. The results of this initial investigation indi- 

 cate that the use of the displacement model method significantly improves theoretical 

 predictions of the measured pressure coefficients on the body surface. However, 

 agreement between measured and predicted pressure coefficients remains poor in the 

 thick stern boundary-layer region over the last 7 percent of the body. Theoretical 

 predictions of the measured mean axial velocity profiles are satisfactory in the 

 thin boundary-layer region, but are generally larger than the measured values when 

 the boundary layer thickens. Refinements in the present displacement body modeling 

 scheme to determine the effective displacement thickness accurately over the entire 

 model surface and wake may improve the pressure distribution predictions in the 

 thick stern boundary layer. 



18 



