Spectral Level Set Methodology in the Design of a Morphing Airfoil

In this paper, we consider the design of a morphing airfoil for improved aileron effectiveness using the spectral level set methodology. This methodology is a framework to formulate topology optimization of interfaces based on the level set methods, which represent the interface as the zero level set of a function. As this function evolves, during the optimization process, topological changes of the interface are easily described. According to our formulation, the Fourier coefficients of the level set function are the design variables of the optimization problem. An advantage of the proposed methodology, for a sufficiently smooth interface, is to admit an error asymptotically smaller than the one for non-adaptive spacial discretizations of the level set function. In this case, the methodology could lead to a reduction of the design space dimension. Another advantage is the nucleation of holes in the interior of the interface.

As an application, we consider an airfoil with a system of actuators distributed along its chord. This system provides morphing capability to the airfoil by operating on its camber to increase lift generation. The optimization problem consists in determining the camber profile that minimizes the actuation power while improving the airfoil effectiveness. The sign of the level set function determines which actuators are activated.