Traditional airfoil parametric technique has significant limitation in modern aerodynamic optimization design.There is a strong demand for developing a parametric method with good intuitiveness, flexibility and representative accuracy. In this paper, two parametric generative schemes based on deep learning methods are proposed to represent the complicate design space under specific constraints. 1. Soft-constrained scheme: The CVAE-based model trains geometric constraints as part of the network and can provide constrained airfoil synthesis; 2. Hard-constrained scheme: The VAE-based model serves to generate diverse airfoils, while an FFD-based technique projects the generated airfoils to the final airfoils satisfying the given constraints. The statistical results show that the reconstructed airfoils are accurate and smooth without extra filters. The soft constrained scheme tend to synthesize and explore airfoils efficiently and effectively, concentrating to the reference airfoil in both geometry space and objective space. The constraints will loose for a little bit because the inherent property of the model. The hard constrained scheme tend to generate and explore airfoils in a wider range for both geometry space and objective space, and the distribution in objective space is closer to normal distribution. The synthesized airfoils through this scheme strictly conform with constraints, though the projection may produce some odd airfoil shapes.
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