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 Cp is specified, increasing
thickness only reduces the lower surface pressures.)
Well, almost. If the upper surface Cp 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.