Numerical Shape Optimization of Subsonic Airfoil Sections
Th. Lutz and S. Wagner
Proceedings ECCOMAS 2000: European Congress on Computational Methods in Applied Sciences and Engineering, September 11-14, 2000, Barcelona, Spain
A tool for the numerical optimization of subsonic airfoil sections has been developed. Contrary to the usual approach, the airfoil geometry is not optimized in a direct way. Instead an inverse conformal mapping procedure is applied to generate the contour and to determine the corresponding inviscid flowfield. The input parameters of this method directly control the local pressure gradient and are used as design variables of the optimization process. Viscous effects are calculated by means of an improved integral boundary-layer procedure. A new approach was developed to efficiently calculate the effects of 'short' transitional separation bubbles. To predict the transition location, a semi-empirical $e^n$-method is utilized. The aerodynamical model has been coupled with a commercial hybrid optimizer to perform numerical shape optimizations of natural laminar flow airfoils. The objective of the present optimizations was to minimize the average drag coefficient for a prescribed range of lift coefficients and Reynolds numbers. Wind-tunnel tests were performed for one of the optimized airfoils and confirmed the theoretical results.