Aerodynamic design via control theory

Computers have had a twofold impact on the science of aerodynamics. On the one hand numerical simulation may be used to gain new insights into the physics of complex flows. On the other hand computational methods can be used by engineers to predict the aerodynamic characteristics of alternative designs. Assuming that one has the ability to predict the performance, the question then arises of how to modify the design to improve the performance. This paper is addressed to that question. Prior to 1960 computational methods were hardly used in aerodynamic analysis. The primary tool for the development of aerodynamic configurations was the wind tunnel. Shapes were tested and modifications selected in the light of pressure and force measurements together with flow visualization techniques. Computational methods are now quite widely accepted in the aircraft industry. This has been brought about by a combination of radical improvements in numerical algorithms and continuing advances in both speed and memory of computers. If a computational method is to be useful in the design process, it must be based on a mathematical model which provides an appropriate representation of the significant features of the flow, such as shock waves, vortices and boundary layers. The method must also be robust, not liable to fail when parameters are varied, and it must be able to treat useful configurations, ultimately the complete aircraft. Finally reasonable accuracy should be attainable at reasonable cost. Much progress has been made in these directions (Murman and Cole, 1971; Jameson, 1974;1987;Jameson and Caughey, 1977; Bristeau et al., 1985; Jameson et al., 1981, 1986;Ni, 1982;Pulliam and Steger, 1985; MacCormack, 1985). In many applications where the flow is unseparated, including designs for transonic flow with weak shock waves, useful predictions can be made quite inexpensively using the potential flow equation (Murman and Cole, 1971;Jameson, 1974; Jameson and Caughen, 1977; Bristeau et al., 1985). Methods are also available for solving the Euler equations for twoand three-dimensional configurations up to a complete aircraft (Jameson et al., 1981, 1986; Ni, 1982; Pulliam and Steger, 1985; MacCormack, 1985; Jameson, 1987). Viscous simulations are generally complicated by the need to allow for turbulence: while the Reynolds averaged equations can be solved by current methods, the results depend heavily on the choice of turbulence models. Given the range of well proven methods now available, one can distinguish objectives for computational aerodynamics at several levels: