Milgram 



Fig. 8 - Schematic view of the outer edge of the 

 boundary layer on the suction side of a section 

 with a mast (A-Airfoil, B- Turbulent region behind 

 the mast, C -Thickening of the boundary layer near 

 the trailing edge, D-Mast) 



semi-empirical boundary layer theory is applied to the region behind a mast, 

 there is no set place to begin the integration and no set values to choose fore 

 and H at this point. Launder (1963) shows that H attains a value between 1.4 

 and 1.5 a short distance aft of his turbulence grid. The momentum thickness 

 is less certain, as it increases rapidly with downstream distance. For the esti- 

 mates made here the integration is started at the leading edge with H equal to 

 1.4 and the momentum thickness equal to the width of the projected thickness of 

 the mast perpendicular to the local flow direction. Figure 6 shows the results 

 of the boundary layer calculations on a high-lift section with and without a mast. 

 The mast reduces the tendency for flow separation. This effect is found on all 

 pressure distributions. 



The Boundary Layer Thickness Correction 



As shown by Van Dyke (1964), the effect of a thin boundary layer on the flow 

 around a body is to yield pressures on the body associated with the potential flow 

 around a shape defined by the body plus the displacement thickness of the bound- 

 ary layer. In the case of an airfoil treated within the framework of linearized 

 theory, the flow can be decomposed into components due to thickness and com- 

 ponents due to camber (see, e.g., Ashley and Landahl, 1965). The flow associated 

 with the thickness yields no lift. For an infinitely thin airfoil all the thickness is 

 due to the displacement thickness of the boundary layer, and the camber is the 

 mean line between the section and the line representing the displacement thick- 

 ness of the boundary layer. For sections without a mast the displacement thick- 

 ness will be significant only near the trailing edge, whereas for sections with a 

 mast there will be significant displacement thickness effects near the leading 

 edge and near the trailing edge. In the design of a section for a given pressure 

 distribution, each point must be moved to windward from the shape calculated 

 by the thin airfoil theory by an amount equal to half the displacement thickness 

 of the boundary layer at that point. 



1420 



