A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



values of Re,^^ from 150,000 to 260,000 for the shear layer in a separation 

 bubble at 61 per cent of the chord on an NACA 663-OI8 airfoil, whereas 

 Gault's values [32] for the same airfoil vary from 160,000 to 380,000. 

 Thus the values of Re^-^ vary from to 380,000, an even wider range than 

 observed for the boundary layer on a plate without pressure gradient. 



One might assume that the large variation is a reflection of the influ- 

 ences of free stream turbulence and pressure gradient on transition of 

 the free shear layer entirely analogous to those demonstrated to exist 

 for boundary layers. However; the available data do not establish this 

 assumption conclusively. The difficulties may be illustrated by Bursnall 

 and Loftin's measurements. Their values of i^et-s vary with the Reynolds 

 number of the airfoil, yet the pressure distribution is substantially inde- 

 pendent of the airfoil Reynolds number. The values of Re^^^ are 148,000, 

 197,000, and 256,000 for airfoil Reynolds numbers of 1.2, 1.7, and 

 2.4 X 10^, respectively. There is no reason to assume that the turbu- 

 lence is greatest at the lowest Reynolds number as would seem to be 

 required if turbulence is the controlling element. 



It appears plausible that the thickness of the boundary layer at the 

 separation point should have some influence on transition, or that a 

 Reynolds number based on the thickness at transition might be more 

 suitable than one based on length of the free shear layer. However, no 

 satisfactory correlation has been established on either basis. Thus in the 

 experiments of Bursnall and Loftin, the values of Re^* at transition are 

 2070, 2560, and 2940 for airfoil Reynolds number of 1.2, 1.7, and 2.4 X 10«. 



Bursnall and Loftin attempted to correlate the results available to 

 them by plotting the ratio of x^ — x^ to 5, against the value of Re^ at 

 separation. (In their paper 5 is the value of y at which u/u^ = 0.707.) 

 The available data fall approximately into two groups, one for regions of 

 separation near the leading edge at high angles of attack, the other for 

 regions of separation near the midchord position at 0° angle of attack. 

 Hence this attempt does not yield an integrated picture. 



Gault [32] attempted further analysis of his measurements and those 

 of Bursnall and Loftin, but the results are not satisfactory. 



Some work on the effect of turbulence was carried out by Gault on 

 the NACA 663-OI8 airfoil. Increased turbulence moved transition up- 

 stream for all conditions and completely eliminated the separation bubble 

 near midchord for all Reynolds numbers from 1.5 to 10 milHon. Separation 

 bubbles near the leading edge were not eliminated but their size was 

 greatly reduced. The effect of increasing the turbulence from 0.2 to 1.1 

 per cent at a Reynolds number of 2 million was approximately the same 

 as increasing the Reynolds number from 2 to 4 milhon at a turbulence 

 level of 0.2 per cent. 



Whereas the values of Re^* for a completely free layer are from 100 to 

 300 as noted in the last article, the values for the separated layers in 



(26) 



