Adjoint-based unsteady shape optimization to suppress transonic buffet

The traditional aerodynamic shape optimization mainly aims at the enhancement of lift-drag ratio in the steady state. In this study, the onset of transonic buffet is improved by the unsteady aerodynamic shape optimization. To achieve this goal, the variance of lift coefficient in a period is adopted as the optimization objective. In addition, the gradients of the objective function with respect to shape parameters are efficiently calculated by the unsteady discrete adjoint method. The proposed method is verified by two optimization examples of NACA0012 and OAT15A. Not only the onsets of transonic buffet are increased by 0.9∘ and 1.7∘ respectively, but also the aerodynamic performance is improved. According to the shape change of optimization examples, we summarize three airfoil geometric characteristics: the position of maximum thickness of the upper airfoil, the thickness near the leading edge, and the thickness near the trailing edge. The influence of the geometric characteristics on the flow stability has been studied.