Aerodynamic optimization of supersonic airfoils using bijective cycle generative adversarial networks

• Supersonic airfoils are obtained by Bicycle-GAN generative model using 6-dimensional parameters. • The proposed Bicycle-GAN model has superior performance to cVAE model in terms of parameterization ability, airfoil generation quality and diversity. • The use of multi-fidelity data for surrogate model reduces the required CFD computational cost. An efficient, diversified, and low-dimensional airfoil parameterization method is critical to airfoil aerodynamic optimization design. This paper proposes a supersonic airfoil parameterization method based on a bijective cycle generative adversarial network (Bicycle-GAN), whose performance is compared with that of the conditional variational autoencoder (cVAE) based parameterization method in terms of parsimony, flawlessness, intuitiveness, and physicality. In all four aspects, the Bicycle-GAN-based parameterization method is superior to the cVAE-based parameterization method. Combined with multifidelity Gaussian process regression (MFGPR) surrogate model and a Bayesian optimization algorithm, a Bicycle-GAN-based optimization framework is established for the aerodynamic performance optimization of airfoils immersed in supersonic flow, which is compared with the cVAE-based optimization method in terms of optimized efficiency and effectiveness. The MFGPR surrogate model is established using low-fidelity aerodynamic data obtained from supersonic thin-airfoil theory and high-fidelity aerodynamic data obtained from steady CFD simulation. For both supersonic conditions, the CFD simulation costs are reduced by >20% compared with those of the cVAE-based optimization, and better optimization results are obtained through the Bicycle-GAN model. The optimization results for this supersonic flow point to a sharper leading edge, a smaller camber and thickness with a flatter lower surface, and a maximum thickness at 50% chord length. The advantages of the Bicycle-GAN and MFGPR models are comprehensively demonstrated in terms of airfoil generation characteristics, surrogate model prediction accuracy and optimization efficiency.