An efficient aerodynamic shape optimization framework for robust design of airfoils using surrogate models

Abstract

This paper deals with developing an efficient Robust Design Optimization (RDO) framework. The goal is to obtain an aerodynamic shape that is less sensitive to small random geometry perturbations and to uncertain operational conditions. The initial shape is the RAE2822 airfoil which is parameterized with 10 design variables. The robust design formulation used is based on an expectation measure. The goal was to minimize the sum of the mean and standard deviation of the drag coefficient of the RAE 2822 airfoil for a given nominal lift coefficient. Here, we focus on improving the methods used for computing the statistics of the aerodynamic performance of the airfoil in every optimization cycle. A relatively small number of samples is evaluated with CFD and used to construct surrogate models based on Kriging and gradient-enhanced Kriging. The aerodynamic performance statistics, which are used to evaluate the robust objective function, are estimated by using quasi Monte Carlo (QMC) sampling with many samples evaluated on the surrogate models. A large number of geometrical uncertainties is parameterized by using a truncated Karhunen-Loève expansion, which enables a significant reduction of the dimensionality of the problem and thus of the surrogate models. By varying the number of samples used to build the surrogate model and by comparing the two types of surrogate modeling methods, it is confirmed that the robust objective function can be evaluated accurately with at most 30 CFD computations and corresponding adjoint computations.