Robust Airfoil Shape Optimization Using Design For Six Sigma

Abstract

Introduction B ECAUSE of the rapid development of computer technologies, tremendous achievement has been made in the computational fluid dynamics (CFD) area during the past few decades. Currently, CFD techniques are widely used not only to simulate and understand complicated flow physics, but also to optimize the aerodynamic shape of air vehicles that enables maximum performance at desired operating conditions. One of the most popular aerodynamic shape optimization algorithms currently available is the gradient-based optimization technique in which a specified objective function is minimized. Sensitivities, the gradients of the objective function with respect to design variables, are used to update the design variables in the direction that the magnitude of the objective function can be reduced in a systematic way. However, application of the aerodynamic shape optimization has been mostly made to single-point optimizations1−4 in which the optimal shape is determined for a specific flight condition. Even though the single-point design optimization guarantees good performance at the specified design point, practical experience indicates that it can lead to a dramatically inferior performance even at a slightly off-design operating condition caused by local gusts or atmospheric disturbances frequently encountered in actual flights. This problem may also occur due to errors involved in manufacturing, which cannot be completely avoided in a practical sense. A straightforward method of avoiding this difficulty is to consider multiple flight conditions simultaneously by constructing the objec-