Shape and parameter optimizations on a high-lift configuration with flap-based circulation control

Circulation control is a prominent active flow control method that can delay the boundary layer transition and enhance aerodynamic performance. However, the coupling of jet and airfoil parameters makes it challenging to derive the optimal parameters based solely on experience. This work employs surrogate-based optimization to optimize the geometric and jet parameters of circulation control on flaps. The standard models CC020-010EJ and NLR-7031 were selected to verify the performance of numerical methods in circulation control and multi-element airfoil, respectively. Model parameterization and grid reconstruction are achieved with pointwise script and free-form deformation. The optimization framework enhances the accuracy of the kriging surrogate model by integrating the generalized hybrid one–two-stage method, the adaptive differential evolution with an optional external archive (JADE) based on successful parent selection (SPS) and the eigenvector-based crossover (EIX) operators (JADE-SPS-EIX) optimization algorithm, and a design space adaptive expansion function. The framework successfully optimized single-objective problems in low dimensions. When the lift coefficient was the objective, it increased by approximately 59.2%. In cases where lift was constrained to improve the lift-to-drag ratio, lift increased by 4.5%, and the lift-to-drag ratio improved by 33.5%. These results demonstrate the framework's capability to optimize circulation control parameters for multi-element airfoils and provide a reference for future high-dimensional, multi-objective active flow control optimizations.