Improving multi-objective optimization of airfoil design with complex optimum method

In our opinion, existing methods for multi-objective optimization of airfoil design either find difficulty with gradient calculations or run into high computation burden. We find that the complex optimum method described by Xie's book^[5] can be employed to obviate gradient calculations and high computation burden. Applying the complex optimum method to our problem, we present an airfoil design method that couples viscous flow analysis with complex optimum method to search for an airfoil with improved aerodynamics at multiple design-points while satisfying specified design constraints. The flow was modeled with Reynolds-averaged Navier-Stokes equations in order to ensure reliable results. In this paper we explain in much detail a multi-point optimization algorithm itself and how to use it to drive the design process efficiently and robustly. In this paper, we give two illustrative numerical examples; the second example is concerned with the minimizations of drags at two design points with three constraints for RAE2822 airfoil as the baseline airfoil. Our optimization approach achieves drag reductions of 12.4% and 4.0% respectively for the two design-points as compared with RAE2822. This example shows preliminarily that our optimization approach looks promising in engineering applications involving specified design constraints.