Integrated Design Optimization of Aerodynamic Shape and Flow Control Parameters for Co-Flow Jet Airfoils

Co-Flow Jet (CFJ) technology is an effective active flow control method for improving aerodynamic performance by enhancing circulation and suppressing flow separation. However, existing CFJ airfoil optimization studies mainly focus on either aerodynamic shape or flow control parameters separately, limiting the exploitation of their coupled effects. This study proposes an integrated optimization framework that simultaneously considers airfoil geometry and CFJ parameters. A combined parameterization method is developed by integrating Class Shape Transformation (CST) for aerodynamic shape representation and adaptive interpolation for CFJ shroud construction. Based on the unified design space, a multi-objective optimization framework using a Kriging surrogate model is established to efficiently optimize the coupled design variables. The proposed method is applied to a NACA6415-based CFJ airfoil, generating 35 Pareto-optimal solutions. Compared with the baseline configuration, the lift-oriented design increases the lift coefficient from 1.53 to 2.26 (47.7%), while the energy-efficiency-oriented design improves the effective lift-to-drag ratio from 37.97 to 75.84. The integrated optimization also outperforms independent shape or flow-control optimization by capturing the nonlinear coupling effects between aerodynamic geometry and jet parameters. This framework provides an effective strategy for the integrated design of CFJ airfoils and other active flow control configurations.