Viscous Airfoil Optimization Using Conformal Mapping Coefficients as Design Variables
Thomas Sorensen · 1991
The XFOIL viscous airfoil design code was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique em-ployed was the Steepest Descent method applied to an Objective/Penalty Function. An important idea of this research is the manner in which gradient information was calculated. The derivatives of the aerodynamic variables with respect to the design variables were cheaply calculated as a by-product of XFOIL's viscous Newton solver. The speed of the optimization process was further increased by updating the Newton system boundary layer variables after each optimization step using the available gradi-ent information. It was determined that no more than 10 of each of the symmetric and anti-symmetric modes should be used during the optimization process due to inaccurate calculations of the higher mode derivatives. Both constant angle of attack and constant lift coefficient optimizations are possible. Multi-point optimization was also developed, although it works best for angle of attack design points. Four example optimizations are documented at the end of this thesis.