Supercritical airfoil flow field prediction: the integration of Transformer and convolutional neural network

Supercritical airfoils play a crucial role in modern civil aviation, where their aerodynamic optimization heavily relies on CFD (computational fluid dynamics) simulations. However, the iterative design process based on CFD is computationally expensive, limiting optimization efficiency. Recent advances in deep learning have demonstrated great potential in flow field prediction, offering a fast and cost-effective alternative to traditional CFD. Existing deep learning-based models primarily employ CNNs (convolutional neural networks) or Transformers, which excel in local feature extraction and global dependency modeling, respectively. However, each method has its limitations in either accuracy or computational efficiency when used independently. Therefore, this study aims to develop an efficient flow field prediction model by integrating CNN and Transformer architectures, thereby enhancing prediction accuracy and generalization capability while reducing computational complexity. The proposed model serves as a powerful auxiliary tool for airfoil aerodynamic optimization.

This study proposed a hybrid deep learning model, TransCNN-FoilNet, designed for rapid flow field prediction of supercritical airfoils. Firstly, CST (Class-Shape Transformation) parameterization was used to define airfoil geometries, and CFL3D solver with SST turbulence modeling was employed to generate a comprehensive dataset covering various angles of attack and relative thicknesses. The model architecture incorporated a ViT (Vision Transformer) encoder to capture global relationships within the flow field, while a U-Net-based CNN decoder reconstructs spatial flow structures, preserving multi-scale information through skip connections. Additionally, this study introduced a weighted L1SSIM loss function, which combines L1 loss and SSIM (structural similarity index measure) to improve predictions in critical regions, such as areas with shock waves. The model was implemented using PyTorch and trained on a large dataset, with performance evaluations conducted across multiple test cases.

Experimental results demonstrate that TransCNN-FoilNet significantly outperforms existing CNN-based and Transformer-based models. Compared to baseline models, U-Net and ViT, it achieves a maximum 79.5% reduction in MAE (mean absolute error). Furthermore, the model reduces lift and drag coefficient prediction errors by up to 90.9%, highlighting its superior accuracy. The weighted L1SSIM loss function further enhances predictive performance, particularly in regions with strong pressure gradients, improving the model's ability to capture complex flow characteristics. Additionally, TransCNN-FoilNet achieves higher computational efficiency compared to Transformer-only models, effectively balancing prediction accuracy, generalization capability, and computational cost. These results indicate that hybrid architectures combining CNNs and Transformers can offer a robust solution for aerodynamic flow field prediction.

This study presented TransCNN-FoilNet, a novel deep learning model that successfully integrates CNN and Transformer architectures for high-accuracy, fast flow field prediction of supercritical airfoils. The model demonstrates superior performance in predicting both flow distributions and aerodynamic coefficients, outperforming existing deep learning models. Additionally, the weighted L1SSIM loss function proves effective in refining predictions in complex flow regions, particularly in shock wave areas. The findings suggest that deep learning has great potential for application in airfoil design and aerodynamic optimization. Future work will focus on further improving computational efficiency, extending the model to three-dimensional flow field prediction, and exploring its applications in unsteady flow analysis and real-time aerodynamic optimization, thereby advancing the integration of deep learning in the field of aerodynamics.