Deep neural network-based reduced-order modeling of high-speed airfoil flow field

The flow field prediction based on deep neural networks has attracted considerable attention in recent years. However, previous studies mainly focused on low-speed and subsonic conditions, whereas much less attention has been paid to reconstructing supersonic and hypersonic flow fields. To rapidly and accurately predict supersonic and hypersonic airfoil flows, this paper proposes a flow field reduced-order model based on deep neural networks, utilizing fully-connected neural and deconvolutional neural networks to establish a mapping relationship between the flow conditions and flow fields. Firstly, a dataset of supersonic airfoil flow fields is constructed by numerical simulations in a wide range of the angles of attack and incoming Mach numbers. Secondly, a deep neural network model is constructed and trained, with the root mean square error of the loss function converged to 0.0019. Finally, the prediction accuracy and generalization performance of the model are analyzed. The root mean square error of the neural network model for the test set is less than 4×10^–3, the maximal relative error is about 0.03, and the correlation coefficients between true and predicted flow fields are higher than 0.99, indicating that the model has good prediction accuracy and interpolation generalization ability. In addition, the neural network model is also able to predict the flow fields for Mach numbers outside the dataset, exhibiting good generalization ability for extrapolated conditions in the range of the Mach number less than 13. Compared to numerical simulations, the prediction speed of the deep-neural-network-based reduced-order model is faster by at least two orders of magnitude, and the efficiency is proportional to the amount of predicted flow fields.