On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization

Abstract

This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-To-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc). The obtained results reveal the accuracy of the derived step length.