Effect of shape parameterization on aerodynamic shape optimization with SPSA algorithm

In this paper several parameterization methods are investigated for two-dimensional airfoils, and applied to aerodynamic shape design optimization problems such as constrained airfoil design. The simultaneous perturbation stochastic approximation (SPSA) method is adopted to estimate the gradients of objective functions that are computed during each design iteration using a finite volume computational fluid dynamics technique for solving compressible Euler equations. The computational results for shape design show that the Hicks-Henne shape functions and NACA orthonormal shape functions perform better than other methods such as Wagner, and B-Spline representation methods, while the B-Spline method can easily adjust the movement by control points.