Theory

Potential-Flow Airfoil Design Method

The airfoil design method is based on conformal mapping. This method differs from other inverse methods in that the velocity distribution is not specified at only one angle of attack. Instead, angles of attack that will result in constant velocity over specified segments of the airfoil are input. In other words, pairs of parameters are specified: the segment of the airfoil and the angle of attack relative to the zero-lift line that will result in constant velocity over that segment. Of course, some matching conditions must be met to guarantee a smooth velocity distribution for all angles of attack. Toward the trailing edge, on both surfaces, a main pressure recovery can be specified. Finally, a short closure contribution must be introduced to ensure that the trailing edge will be closed.

In reality, the segments corresponding to the various input angles of attack are not specified in the airfoil plane but rather in the conformal-mapping plane in which the airfoil is represented by a circle. No difficulties have arisen in correlating the arcs of the circle with the segments of the airfoil. An option has been included that allows a transition ramp to be specified by only two points, a forward and an aft limit, relative to the beginning of the pressure recovery.

It should be remembered that for any given velocity distribution there does not necessarily exist a "normal" airfoil. For example, the closure contributions could be quite large, which would result in a very large trailing-edge angle. The closure contributions could also give rise to a region of negative thickness near the trailing edge. Accordingly, several iteration options have been included that allow the trailing-edge angle to be specified while certain input angles of attack or the amount of pressure recovery is iterated.

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