Airfoil-based convolutional autoencoder and long short-term memory neural network for predicting coherent structures evolution around an airfoil

Airfoil stall induced by unsteady flow separation is a major inhibitor that constrains the aircraft design. Hence, it is critical to have a better understanding of the flow dynamics around the airfoil near stall conditions. Recently, machine learning (ML) has been widely used to predict the spatiotemporal evolutions of coherent structures over the airfoil. Nonetheless, due to the existence of strong nonlinearity introduced by turbulence, most of the existing approaches focus on prediction of the flow fields in the laminar flow regime. In this work, we seek to examine the applicability of deep neural network (DNN) to prediction of turbulent flows around a NACA (National Advisory Committee for Aeronautics) 4412 airfoil. Large eddy simulations (LES) are performed to prepare the training dataset. Both proper orthogonal decomposition (POD) and DNN-based reduced-order models (ROM) are employed for reconstructing the flow fields. A convolutional autoencoder (CAE) is applied to map the high-dimensional flow dynamics into the low-dimensional nonlinear manifold. The geometric features are considered in the input matrix of the CAE network by setting physical quantities inside the airfoil to zero to reflect the physics. Then, the multi-head attention-strengthened long short-term memory (MH-LSTM) is utilized to predict the evolutions of latent vectors. Finally, the high-dimensional flow dynamics can be reconstructed by utilizing the decoder part of CAE. We believe that the MH-LSTM methodology provides a promising path towards predicting the unsteady flow field over the airfoil by capitalizing on the capability of multi-head attention allowing for attending to distinct parts of input sequence.