16 



R^^C-f R, 



[48] 



Owing to the presence of the arbitrary constant C, it is obvious that Mangler's transformations 

 are not sufficient to determine the critical values of the Reynolds numbers for transition. 

 Hence, other considerations must apply. In the analysis of the stability of laminar flows on 

 bodies of revolution, it was found^'"^^ that the resulting linearized equation of the disturbed 

 flow at the limiting condition of large Reynolds numbers was the same as that for two-i 

 dimensional flows. Hence 



^d.N ~ ^d.N 



[49] 



and as stated previously, the neutral stability chart of Figure 3 is applicable to both two- 

 dimensional and axisymmetric flows on bodies of revolution. As a first approximation a 

 similar condition will be assumed to hold for self-excited transition. Then 



^d, ts ^ ^d, ts 



[50] 



As a check on the essential validity of the preceding, the self-excited transition points 

 were computed for Lyon's'^^ bodies of revolution on the basis of Figure 4. Owing to the non- 

 existance of low-turbulence wind tunnels at the time of Miss Lyon's tests, the condition of 

 least degree of turbulence represented in her tests was that when the turbulence-producing 

 screens were not inserted in the wind tunnel. Comparison is then made in Table 1 of the axial 

 locations l/L of the computed neutral stability points and self-excited transition points with 

 the test data for the no-screen condition. 



TABLE 1 



Axial Locations l/L of Transition Data for Lyon's Bodies of Revolution-^^ 



Subject 



r^odel A 

 /r^ = 2.09x10^ 



Model B 

 ff^ =2.075x10^ 



Computed Neutral Stability Point 



0.20 



0.13 



Computed Self-Excited Transition Point 



0.56 



0.7 



Measured Transition Region 

 (without screen) 



0.50-0.70 



0.30-0.35 



Regions of Favorable Pressure Gradient 



- . 30 



0-0.13 

 0.40-0.61 



Regions of Adverse Pressure Gradient 



0.30-1 



0.13-0.40 

 0.61- 1 



