Generalized multipoint inverse airfoil design

In a rather general sense, inverse airfoil design can be taken to mean the problem of specifying a desired set of airfoil characteristics, such as the airfoil maximum thickness ratio, pitching moment, part of the velocity distribution, or boundary-layer development. From this information, the corresponding airfoil shape is determined. This paper presents a method that approaches the design problem from this perspective. In particular, the airfoil is divided into segments along which, together with the design conditions, either the velocity distribution or boundary-layer development may be prescribed. In addition to these local desired distributions, single parameters like the airfoil thickness can be specified. Determination of the airfoil shape is accomplished by coupling an incompressible potential-flow inverse airfoil design method with a direct integral boundary-layer analysis method. The resulting system of nonlinear equations is solved by a multidimensional Newton iteration technique. An example airfoil design, not intended for practical application, is presented to illustrate some of the capabilities of the method. As this example illustrates, the design methodology presented provides a means of dealing simultaneously with the myriad requirements and constraints that can be specified in the design of an airfoil.