Multi-objective robust airfoil optimization based on non-uniform rational B-spline (NURBS) representation

Abstract

In order to improve airfoil performance under different flight conditions and to make the performance insensitive to off-design condition at the same time, a multi-objective optimization approach considering robust design has been developed and applied to airfoil design. Non-uniform rational B-spline (NURBS) representation is adopted in airfoil design process, control points and related weights around airfoil are used as design variables. Two airfoil representation cases show that the NURBS method can get airfoil geometry with max geometry error less than 0.0019. By using six-sigma robust approach in multi-objective airfoil design, each sub-objective function of the problem has robustness property. By adopting multi-objective genetic algorithm that is based on non-dominated sorting, a set of non-dominated airfoil solutions with robustness can be obtained in the design. The optimum robust airfoil can be traded off and selected in these non-dominated solutions by design tendency. By using the above methods, a multi-objective robust optimization was conducted for NASA SC0712 airfoil. After performing robust airfoil optimization, the mean value of drag coefficient at Ma0.7–0.8 and the mean value of lift coefficient at post stall regime (Ma0.3) have been improved by 12.2% and 25.4%. By comparing the aerodynamic force coefficients of optimization result, it shows that: different from single robust airfoil design which just improves the property of drag divergence at Ma0.7–0.8, multi-objective robust design can improve both the drag divergence property at Ma0.7–0.8 and stall property at low speed. The design cases show that the multi-objective robust design method makes the airfoil performance robust under different off-design conditions.