A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



numbers. According to Dunn and Lin the critical wall to free stream 

 temperature ratio T^^/T^ required for complete stability with respect to 

 two-dimensional disturbances is 1.6 at a Mach number of 3, 1.7 for 

 M^ = 4, and zero at M^ = 7.5. Stability with respect to waves traveling 

 at an angle to the flow direction varies with this angle. At a Mach num- 

 ber of 4 the required ratio varies between 1.47 and 1.7 for angles of 0° to 

 74° to the stream direction and falls abruptly to zero for angles of 75° or 

 more. 



The value of Ty,/T„ at which there is no heat transfer to or from the 

 body varies with the Mach number. To bring out the heat transfer rela- 

 tionships more clearly, it is better to use the ratio (Tw — Tj)/Tl where 



0.2 



H 



H^ 



OO) 



-0.4 



-0.6 



-0.8 



1.0 



4 



M 



Fig. A,26a. Theoretical values of (Tw — T^)/Tl for complete stabilization of bound- 

 ary layer against two-dimensional disturbances according to Dunn and Lin. 



Tr is the recovery temperature and Tl is the stagnation temperature. 

 The relation between the two ratios is as follows : 





= R 



o 



r(l - R) - R 



where R is the ratio r«/T« (equal to 1/(1 + 0.2 Ml) for isentropic flow) 

 and r is the recovery factor (0.851 for the laminar boundary layer in air). 

 Fig. A,26a shows the Dunn and Lin values for complete stabihzation 

 against two-dimensional disturbances plotted in terms of (Tw — T^/Tl 

 and the Mach number M. 



Fig. A,26b shows the results of the more systematic measurements of 

 transition Reynolds number as a function of (Tw — T,)/T°. The data 

 which have been omitted from the figure relate to effects of heating only, 

 to experiments on artificially roughened bodies, and to experiments over 



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