A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



that for elements close to the leading edge (closer than 25 times the rough- 

 ness height) and that for which transition is at the roughness element 

 itself. There remain systematic variations with roughness location, but 

 the anomalous features (regions in which the ratio increases with increas- 

 ing roughness height) of Brinich's figure [106, Fig. 12] disappear. 



The data for supersonic flow are displaced to values of k/b* about 

 3 times those for incompressible flow. This ratio is of the order of magni- 

 tude of the ratio of the free stream density to that of the air near the 

 surface striking the roughness element. One might speculate that the 

 smaller effect is associated with the smaller air density at the element. 



Brinich made additional experiments [107] on a cylinder for which the 

 leading edge radius was 0.001 inch as compared with 0.008 inch for the 

 earlier measurements. These indicated somewhat greater sensitivity to 

 roughness, the recomputed points falling at the lower edge of the scatter 

 band in Fig. A,25c. The Reynolds numbers for the smooth cyUnder based 

 on maximum surface temperature were 1.7 million and 3.6 milHon, respec- 

 tively. The leading edge Reynolds numbers were 286 and 2900. The 

 minimum surface temperature was found at Reynolds numbers of 0.8 

 milhon and 1.2 million, respectively. 



Sinclair and Czarnecki [97] made measurements on a 10° cone at 

 Mach numbers of 1.41, 1.61, and 2.01 with a single two-dimensional 

 roughness strip consisting of a |^-inch wide band of 0.003-inch thick cellu- 

 lose tape at various locations. These tests gave the surprising result that 

 the decrease in transition Reynolds number was even greater than that 

 experienced for the same value of roughness height to displacement thick- 

 ness in low speed tests, i.e. below the low speed correlation curve of Fig. 

 A,25c. Obviously more data are needed on roughness effects over a wider 

 range of Mach number, body shape, and roughness element shape. It is 

 possible that the shock wave configuration and shock-induced separation 

 are more important than the ratio of roughness height to boundary layer 

 displacement thickness. 



The effects of roughness near the conical tip of cone-ogive-cylinder 

 models on transition were studied by Luther [114]- He states that an 

 attempted correlation on the basis of k/b* was unsuccessful. This is not 

 surprising in view of the effects of pressure gradient produced by the 

 body shape. 



Luther was primarily interested in roughness as a means of fixing 

 boundary layer transition. He used distributed roughness as well as trip 

 wires to determine the minimum roughness height needed to produce 

 transition at the element. Large Mach number effects were found, the 

 critical heights for a Mach number of 4.09 being about 3 to 4 times that 

 for a Mach number of 1.64. As in the case of Brinich's data the effect of 

 the low density in reducing the value of the Reynolds number Ukk/v seems 

 to account for the Mach number effect. 



< 62) 



