Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

Abstract

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: 1) the demand for significant efficiency improvements over current design methods; 2) a general and flexible three-dimensional surface representation; and 3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: .1) employing fully implicit (Newton) methods for the CFD analyses; 2) adopting a Bezier-Bernstein polynomial parameterization of two-and three-dimensional surfaces; and 3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficienVdesign strategies in current use.The new aerodynamic shape optimization procedure is demonstrated in the design of both two-and three-dimensional inviscid aerodynamic problems including a two-dimensional L&

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