A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



More recent studies have been made by Fage and Preston [74] in a 

 water stream using the fluid motion microscope, but these do not agree 

 so well with the two-dimensional values of Fig. A, 2b. One of the bodies 

 used was a long cylinder 3 inches in diameter with a semi-ellipsoidal 

 nosepiece 6 inches long, and the water stream was 7 inches in diameter. 

 Most of the observations were taken with turbulence screens about a 

 foot ahead of the nose of the body. The turbulence varied considerably 

 along the length of the body, and if the local value at the transition point 

 is used as abscissa in Fig. A,2b, the values of Re^ are of the order of 

 |- to -g- those observed for the flat plate. It is obvious that the higher 

 turbulence levels upstream are influencing the location of transition. 

 Even if the average turbulence level from the nose to the transition point 

 is used, the values still fall below the flat plate values, although the pres- 

 sure distribution is mildly favorable and should yield higher values. As in 

 many early experiments on transition it is possible that effects of surface 

 waviness may have been present. At any rate the values observed for 

 Rst for a turbulence level of approximately one per cent were of the order 

 of 300,000 to 400,000 as compared with the 600,000 to 700,000 for the 

 flat plate shown in Fig. A,2b. 



Fage and Preston also studied transition on a second body with the 

 same semi-ellipsoidal nose shape, a 4-inch cylindrical mid-body section, 

 and a tail tapering in diameter from 3 to 2 inches over a length of 16 

 inches. For this body, transition occurred following laminar separation 

 and the phenomena observed were similar to those described in Art. 16. 



The boundary layer on a body of revolution is of course not compa- 

 rable with that on a plate at the same distance from the stagnation point 

 because of the three-dimensional character of the flow. Mangier [75] has 

 obtained a general relationship between two-dimensional and axially sym- 

 metrical boundary layers. When apphed to compute the relation between 

 the distance Xi along the axis of the body of revolution and the distance x 

 along a flat plate at which the boundary layer thickness is identical for 

 the two bodies, we find 



''{x)dx 



\x,) 



where r{x) is the radius of the body of revolution at axial distance x. Thus 

 X is less than xx over the forward part of the body, equal at some point 

 beyond the maximum cross section, and exceeds it near the rear end 

 where r{x) is diminishing rapidly, causing a rapid thickening of the 

 boundary layer from continuity considerations. The equivalent flat plate 

 Reynolds number of transition differs from Rbx^ in the same way. 



Measurements of transition on a prolate spheroid of fineness ratio 9 

 and on a modified prolate spheroid of fineness ratio 7.5, modified to give 

 more favorable pressure gradients over the nose, were made by Boltz, 



(48 > 



