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The modern aerodynamic optimization has a strong demand for parametricmethods with high levels of intuitiveness, flexibility, and representativeaccuracy, which cannot be fully achieved through traditional airfoil parametrictechniques. In this paper, two deep learning-based generative schemes areproposed to effectively capture the complexity of the design space whilesatisfying specific constraints. 1. Soft-constrained scheme: a ConditionalVariational Autoencoder (CVAE)-based model to train geometric constraints aspart of the network directly. 2. Hard-constrained scheme: a VAE-based model togenerate diverse airfoils and an FFD-based technique to project the generatedairfoils onto the given constraints. According to the statistical results, thereconstructed airfoils are both accurate and smooth, without any need foradditional filters. The soft-constrained scheme generates airfoils that exhibitslight deviations from the expected geometric constraints, yet still convergeto the reference airfoil in both geometry space and objective space with somedegree of distribution bias. In contrast, the hard-constrained scheme producesairfoils with a wider range of geometric diversity while strictly adhering tothe geometric constraints. The corresponding distribution in the objectivespace is also more diverse, with isotropic uniformity around the referencepoint and no significant bias. These proposed airfoil parametric methods canbreak through the boundaries of training data in the objective space, providinghigher quality samples for random sampling and improving the efficiency ofoptimization design.

Parametric Generative Schemes with Geometric Constraints for Encoding and Synthesizing Airfoils