Comparison of three geometric representations of airfoils for aerodynamic optimization

Abstract

Three geometric representation methods for airfoils are compared for the design and optimization of turbomachinery cascades by an adjoint equation method. They are the PARSEC method, the Hicks-Henne shape function method, and the mesh-point method. Two-dimensional, transonic, and inviscid inverse design problems are studied. Comparisons are made for three different configurations including the NACA0015 airfoil, the 10th standard configuration compressor blade, and the VKI turbine nozzle blade. Gradient information for optimization is obtained by using a continuous adjoint equation method based on the Euler equations. Conjugate gradient method is adopted as the optimization scheme. The results suggest that the PARSEC method is not suitable for representing cascade blade shapes, the Hicks-Henne shape function method converges to the optimum faster than the mesh-point method does, but the mesh-point method can reach higher accuracy. © 2003 by the authors.