Knowledge-Based Airfoil Shape Optimization Using Space Mapping

Abstract

A computationally efficient optimization methodology for transonic airfoil design is presented. A direct optimization of the expensive high-fidelity computational fluid dynamics (CFD) airfoil model is replaced by an iterative updating and re-optimization of a cheap surrogate model. The surrogate is constructed using the low-fidelity model which is based on the same governing fluid flow equations as the high-fidelity model, but uses coarser mesh resolution and relaxed convergence criteria. The low-fidelity model undergoes suitable corrections to become a reliable representation of the high-fidelity one so that it can be subsequently used to find an approximate optimum design of the latter. The corrections are implemented using space mapping. To our knowledge, it is one of the first applications of space mapping to aerodynamic shape optimization. Our method is applied to constrained airfoil lift maximization and drag minimization in two-dimensional inviscid transonic flow. The optimized designs are obtained at substantially lower computational cost when compared to the direct high-fidelity model optimization.