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1992

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NASA TechnicalPaper 3260

1992

An Approach to Constrained Aerodynamic Design With Application to Airfoils

Richard Langley Hampton,

L. Campbell Research Virginia Center

National Aeronautics Space Administration Office of Management

and

Scientific and Technical Information Program

Summary An approach has been developed for incorporating flow and geometric constraints into the DirectIterative Surface Curvature (DISC) design method. In this approach, an initial target pressure distribution is developed using a set of control points. The chordwise locations and pressure levels of these points are initially estimated either from empirical relationships and observed characteristics of pressure distributions for a given class of airfoils or by fitting the points to an existing pressuredistribution. These values are then automatically adjusted during the design process to satisfy the flow and geometric constraints. The flow constraints currently available are lift, wave drag, pitching moment, pressure gradient, and local pressure levels. The geometric constraint options include maximum thickness, local thickness, leadingedge radius, and a "glove" constraint involving inner andouter bounding surfaces. This design method has also been extended to include the successive constraint release minimization. A number of test (SCR) approach to constrained

make them a viable design applications.

option

for

many

research

and

A natural extension of these analysis capabilities is the development of related automated design methods. These design methods may bedivided into two general categories: (1) methods that employ an inverse solver in at least part of the computational domain, and (2) methods that utilize direct analyses in an iterative manner. Classical inverse codes, such as those of Giles and Drela (1986) and Volpe and Melnik (1985), and the fictitious-gas method of Sobieczky et al. (1979) are examples of the first category. Numericaloptimization (Hicks, Murman, and Vanderplaats 1974) and the Direct Iterative Surface Curvature (DISC) method of Campbell and Smith (1987a, 1987b) fall into the second category. These direct approaches can be coupled with any analysis method and thus take advantage of the experience and confidence levels already established for the chosen code. Since they are also relatively easy to couple with existinganalysis codes, a designer can utilize the latest computational technology. Good overviews as well as many individual examples of the state of the art of automated design methods are given in Anon. (1990a) and in Anon. (19905). As noted by Dulikravich (1990), the design problem most often addressed by automated design methods is that of obtaining the geometry that will yield a specified surfacepressure or velocity distribution. Two exceptions to this are the fictitious-gas method and the optimization to a global objective function such as drag. In the fictitious-gas approach, a shockfree supercritical flow is obtained; however, no direct control is available over either the surface pressures or geometry. The use of a global objective function in optimization (to minimize wave drag, forexample) is attractive in that it deals directly with the parameters of interest for design. Unfortunately, the global parameter most often used (drag) is also the one that is generally the least accurately calculated and is slow to converge. This means that long run times may be required to get sufficiently accurate sensitivity derivatives for use in the optimizing routines. Also, the results obtained...