B,25 • THREE-DIMENSIONAL EFFECTS 



juncture between a wing and a body. Attention has already been called 

 to the fact that three-dimensional effects are hard to avoid in regions of 

 adverse pressure gradient. They become very pronounced in regions of 

 flow separation. On low aspect ratio wings at large angles of attack, 

 separation often manifests itself as a curving of the flow in a continuous 

 fashion to form the large scale trailing vortices. Important as these cases 

 are, we shall regard them as special problems beyond the scope of the 

 present treatise. 



Some mention will be made of a particular three-dimensionality known 

 as yawed flow. This is the condition where the leading edge of a two- 

 dimensional body is at an angle other than normal to the mean flow, 

 such as might be represented by an infinitely long swept wing. In such 

 cases deviations from the mean flow direction occur in the boundary layer. 

 Among the first quantitative measurements to show the effects on swept 

 wings are those of Kuethe, McKee, and Curry [105]. 



In the case of laminar yawed flow it is well known, and readily shown 

 by the equations of motion, that the boundary layer development with 

 distance normal to the leading edge and the velocity components associ- 

 ated with this direction are independent of yaw. In other words, bound- 

 ary layer thickness and velocity profiles, based on the stream component 

 normal to the leading edge are independent of the flow parallel to the 

 leading edge. This is known as the "independence principle." 



According to the best evidence at hand, the independence principle 

 does not apply in turbulent flow. The experiments of Ashkenas and Rid- 

 dell [106] conducted on yawed flat plates show that the thickness of the 

 turbulent boundary layer at a given streamwise distance from the lead- 

 ing edge increases with the angle of yaw. A 1-inch strip of sandpaper 

 glued to the surface near the leading edge made turbulent flow a cer- 

 tainty from that point on and gave an essentially fixed virtual origin for 

 the boundary layer. In terms of distance ^ from the virtual origin parallel 

 to the free stream direction, the displacement thickness 5* was found to 

 be given by 



0.046? 



(cos d)i 



iw 



where d is the yaw angle. Except for the factor (cos 6)^, this is the ordi- 

 nary expression for 5* in terms of wall length traversed by the flow. 

 According to Ashkenas and Riddell, yawing would have the effect of 

 decreasing 5* at a given streamwise distance if the independence princi- 

 ple were to apply. The arguments leading to this conclusion are left to 

 the original paper. 



The above result is in disagreement with that of Young and Booth 

 [107] who concluded that the independence principle does apply in the 



< 157) 



