A Fast Prediction Model of Supercritical Airfoils Based on Deep Operator Network and Variational Autoencoder Considering Physical Constraints

Flow field prediction is crucial for evaluating the performance of airfoils and aerodynamic optimization. Computational fluid dynamics (CFD) methods usually require a considerable amount of computational resources and time. In this study, a composite model based on deep learning is proposed for flow field prediction. The variational autoencoder (VAE) model is designed to extract representative features of flow fields. The VAE model is trained to determine the optimal latent variable dimension and Kullback-Leibler (KL) divergence weight. Several physical constraints based on mass conservation and pressure coefficient are introduced to reduce the reconstruction loss and improve the model generalization ability. A DeepONet-MLP model, which combines a deep operator network (DeepONet) and a multilayer perceptron (MLP), is trained to achieve the nonlinear mapping from airfoil shapes and lift coefficients to latent variables in the VAE with fewer parameters. Eventually, a DeepONet-MLP-VAE model, which connects the decoder in VAE with DeepONet-MLP, is applied for fast flow field prediction. The results show that the proposed model can accurately and efficiently predict the transonic flow field, with a mean absolute error of 0.0016 and an average processing time of 0.010 s per flow field, which significantly accelerates the CFD evaluation process.