Orthonormal functions for airfoil and wing parametrization

Abstract

In an attempt to reduce the expenditure associated with aerodynamic shape optimization, the suitability of orthonormal functions for an efficient, accurate, and user-independent parametrization of twoand three-dimensional aerodynamic shapes is explored, To permit assessment of a variety of such functions, they were numerically generated. The construction of the orthonormal functions accommodates geometric constraints as they typically occur in aerodynamic shape optimization. The relative performance of several orthonormal functions is demonstrated for applications to the NACA 0012 airfoil and to two unconventional airfoils. Three-dimensional configurations such as the ONERA-M6 wing and a wing for a supersonic transport aircraft were directly parametrized using orthonormal functions of two independent variables. The applications make a strong case for further pursuing orthonormal functions for geometry representations in aerodynamic shape optimization. Introduction In aerodynamic shape optimization, a configuration is specified by a set of design variables (e.g., twist, camber, thickness distribution). The changes in the aerodynamic characteristics of the subject configuration with variations in these design variables are called sensitivities. They can be evaluated with, for instance, direct,l adjoint,2 or o n e ~ h o t ~ methods. These sensitivities are fed to an optimizer that selects values of the design variables for which a criterion of merit (such as lift, drag, lifvdrag, etc.) is optimal. The more complete the control over the geometric definition of the configuration is (Le., the wider the design space is), the more effective this optimization process will be. For example, directly shaping the wing contour will lead to a wider class of wing shapes than manipulating the wing shape through variations in parameters such as twist, camber, thickness, etc. There has been a long quest for efficient and accurate means for representing aerodynamic shapes. Shape function^,^?^ if judiciously chosen and placed, proved *Principal Engineerkientist. High Speed Aerodynamics tManager. High Speed Aerodynamics Technology. Technology. Senior Member AIAA. Associate Fellow AIAA. Copyright