Robust Airfoil Optimization to Achieve Consistent Drag Reduction Over a Mach Range ^{∗}

Wu Li^{†}, Luc Huyse^{‡}, and Sharon Padula^{§}

June 22, 2001

Abstract

We prove mathematically that in order to avoid point-optimization at the sampled design points for multipoint airfoil optimization, the number of design points must be greater than the number of free-design variables. To overcome point-optimization at the sampled design points, a robust airfoil optimization method (called the profile optimization method) is developed and analyzed. This optimization method aims at a consistent drag reduction over a given Mach range and has three advantages: (a) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it allows a designer to make a trade-off between a truly optimized airfoil and the amount of computing time. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.

∗This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-97046 while the first two authors were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23681.

†Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529 wli@odu.edu.

‡ICASE, NASA Langley Research Center, Hampton, VA 23681 luc@icase.edu.

§MDO Branch, NASA Langley Research Center, Hampton, VA 23681 S.L.PADULA@LaRC.NASA.GOV.