A, 5 • SURFACE ROUGHNESS AND WAVINESS 



conditions in which transition occurs downstream from the roughness ele- 

 ment. Appreciable effects of roughness occur for roughness elements of 

 height equal to 0.2 to 0.4 the displacement thickness of the boundary 

 layer at the roughness element depending on the turbulence level. At a 

 certain value of k/b* which depends on many quantities, including the 

 speed, location of the roughness element, and air stream turbulence, the 

 transition position in its forward motion reaches the roughness element 

 and remains there. The curve of Fig. A,5h does not apply after transition 

 reaches the roughness element. 



Fig. A,5i. Effect of spherical roughness elements on the transition Reynolds num- 

 ber of a plate. Measurements of Klebanoff, Schubauer, and Tidstrom [2S\. 



As contrasted with this behavior of two-dimensional roughness ele- 

 ments, the data on three-dimensional elements correlate best with the 

 assumption of a critical Reynolds number of the roughness element. Ex- 

 periments have been made by Klebanoff, Schubauer, and Tidstrom [23] 

 on single rows of spherical elements of various spacings at various dis- 

 tances from the leading edge of a flat plate. The results are shown in 

 Fig. A,5i and A,5j, showing Re^ vs. fc/6* and Re^, vs. Ukk/v respectively, 

 where Uk is the velocity in the boundary layer at a distance k from the 

 wall. There is considerable scatter, but from the results for the smallest 

 spheres the surface may be considered aerodynamically smooth, i.e. the 



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