High Lift Airfoil Design

To produce high lift coefficients, we require very negative pressures on the upper surface of the airfoil. The limit to this suction may be associated with compressibility effects, or may be imposed by the requirement that the boundary layer be capable of negotiating the resulting adverse pressure recovery. It may be shown that to maximize lift starting from a specified recovery height and location, it is best to keep the boundary layer on the verge of separation*. Such distributions are shown below for a Re of 5 million. Note the difference between laminar and turbulent results.

The thickest section at Re = 10 million is 57% thick, but of course, it will separate suddenly with any angle of attack.

For maximum airfoil lift, the best recovery location is chosen and the airfoil is made very thin so that the lower surface produces maximum lift as well. (Since the upper surface C_p is specified, increasing thickness only reduces the lower surface pressures.)

Well, almost. If the upper surface C_p is more negative than -3.0, the perturbation velocity is greater than freestream, which means, for a thin section, the lower surface flow is upstream. This would cause separation and the maximum lift is achieved with an upper surface velocity just over 2U and a bit of thickness to keep the lower surface near stagnation pressure.

A more detailed discussion of this topic may be found in the section on high lift systems.

*This conclusion, described by Liebeck, is easily derived if Stratford's criterion or the laminar boundary layer method of Thwaites is used. For other turbulent boundary layer criteria, the conclusion is not at all obvious and is almost surely not generally valid.