Optimal Design of a Morphing Airfoil using Spectral Level Set Methodology

1. Abstract A desirable feature in multidisciplinary design optimization is to achieve an acceptable preliminary or initial design in an expeditiously fashion. One way to pursue this goal is to decrease the number of design variables assigned to structural definition. To accomplish this reduction the optimization problem is formulated following the Spectral Level Set Methodology. According to this formulation, an interface is described as a level set of a function. As this function evolves, during the optimization process, topological changes of the interface may occur. By using the Fourier coefficients of the level set function as design variables, a major reduction of the design space dimensionality is achieved. In this paper, a system of actuators provides morphing capability to an airfoil by operating on its mean camber to produce an additional amount of lift. The problem consists in determining the airfoil profile that minimizes the power consumption while improving the airfoil effectiveness. We show the spectral level set methodology can adequately handle the occurrence of spike-like functions during the optimization process with a very small number of Fourier coefficients, thus enhancing the performance of multidisciplinary design tools. 2.