Control parameter layout of compressor airfoils and adaptive optimization method for boundary extension

Parameterized optimization methods are effective approaches for achieving high aerodynamic performance in compressors. Traditional parameterized optimization methods rely on a designer's preselected control parameter layout (including control frame orientation, point density distribution, control point displacement direction, number of variables, and variable ranges), which are purely based on empirical knowledge without sufficient theoretical basis. This paper selects the free-form deformation (FFD) method and Bayesian algorithm as the parameterization method and optimization algorithm for compressor airfoil optimization and studies the influence of FFD control parameter layouts on aerodynamic optimization performance. Additionally, an adaptive optimization method for control parameters based on FFD is proposed, where the orientation and density of the control framework can be incorporated as variables into the control parameters. During the optimization process, the range of design variables is adaptively expanded. A comparison between FFD optimization results based on B-spline and Bernstein basis functions shows that the former achieves an average performance improvement of 4% relative to the latter. Furthermore, an optimization method with an infinitely expandable boundary based on Bernstein basis FFD is proposed, which improves the performance by 12% compared to general adaptive boundary expansion methods.