GIFT Songan Zhang 's Team Publishes in Aerospace Science and Technology

Traditional computational fluid dynamics methods achieve high accuracy in simulating compressor cascade flow fields, but their high computational cost and limited efficiency make it difficult to meet the demand for rapid analysis under multi-physical operating conditions. Deep learning methods offer new pathways for predicting complex flow fields with their powerful nonlinear modeling capabilities. However, in the domain of compressor cascade flow field modeling, systematic research and comparative analysis of different deep learning model structures remain limited. This is particularly true for complex turbulent flow modeling under multi-physical parameter coupling, where the encoding strategies for physical conditions and their collaborative design with model structures lack sufficient comparative study. This gap impedes the reliable application of deep learning methods to complex compressor cascade flow field modeling.

To address this issue, Associate Professor Song'an Zhang at the Global Institute of Future Technology, SJTU, in collaboration with the School of Aeronautics and Astronautics, published a paper titled "Comparative study of neural structure paradigms for compressor cascade flow field modeling based on the condition-encoder" in the journal Aerospace Science and Technology. The researchers leveraged U-Net neural networks and FNO neural operators, incorporating both learning-based and non-learning-based condition encoders to achieve high-precision and rapid modeling of compressor cascade flow fields. They systematically analyzed the modeling performance of different deep learning models combined with condition encoding strategies, offering insights and guidance on selecting deep learning models and co-designing parameter embedding strategies for compressor cascade flow fields under varying physical parameters.

The paper proposes the Condition-Encoder U-Net (CEU-Net) and Condition-Encoder FNO (CEFNO), two deep learning models that integrate condition encoding mechanisms based on the concept of physical parameter embedding. This framework enables efficient and accurate modeling of complex compressor cascade flow fields and systematically evaluates the influence of different model structures and condition embedding strategies on modeling accuracy and performance. The research findings close the gap in the systematic evaluation of physical parameter embedding strategies for complex flow field modeling, providing valuable conclusions and methodological foundations for the design and selection of physics-informed deep learning models.

Figure 1 and Figure 2 illustrate the structures of CEU-Net and CEFNO, respectively. Figure 3 presents the learning-based and non-learning-based condition encoders, which explicitly embed flow field physical parameters, such as inlet Mach number and incidence angle, into the deep learning models to achieve high-precision modeling of compressor cascade flow fields under varying geometric and multi-physical operating conditions.

Figure 1-Schematic diagram of CEU-Net structure

Figure 2-Schematic diagram of CEFNO structure

(a) Learning-based condition encoder structure (LCE)

(b) Non-learning-based condition encoder structure (NLCE)

Figure 3-Structure of the condition encoder

By analyzing the CEU-Net and CEFNO models, the researchers found that both achieve high-precision flow field modeling, with root mean square errors below 2%. A comparison of the flow field prediction distribution contours in Figures 4–6 reveals that, compared to velocity fields, pressure fields exhibit smoother distribution characteristics and relatively lower spatial gradients. This makes it easier for deep learning models to learn their distribution patterns and achieve stable predictions. In contrast, velocity fields show strong shear and significant nonlinear effects in regions such as boundary layers, separation zones and wakes, with dramatic local velocity gradient variations. This leads to concentrated errors, increasing the difficulty for the models to learn the velocity distribution.

Figure 4-Comparison of pressure field (P) predictions

Figure 5-Comparison of velocity field (U) predictions

Figure 6-Comparison of velocity field (V) predictions

Figure 7-Comparison of C_p distribution predictions

Regarding super-resolution prediction, the combination of FNO's global frequency-domain modeling characteristics and NLCE's grid-resolution-invariance embedding mechanism enables NLCEFNO to perform super-resolution prediction. However, the results in Figures 8-11 indicate that as the input grid resolution increases, discretization mismatch errors gradually accumulate, leading to an increase in overall modeling error. This error growth trend is particularly prominent in the regions of flow field with large gradients.

Figure 8-Comparison of root mean square error for super-resolution prediction.

Figure 9-Comparison of super-resolution prediction results for pressure field P.

Figure 10-Comparison of super-resolution predictions for the velocity field U.

Figure 11-Comparison of super-resolution predictions for velocity field V.

This study reveals the structural differences between CEU-Net and CEFNO and the influencing mechanisms of condition embedding strategies. The results indicate that across different complex flow regions, the design and selection of the condition encoder must align with the deep learning model structure to achieve high-precision modeling of complex compressor cascade flow fields.

Paper link:
https://doi.org/10.1016/j.ast.2025.111527

Author Profile

Honglin He
Ph.D. student (Class of 2024), SJTU. Research interests: AI for compressor flow field prediction and analysis, intelligent aerodynamic modeling.

Hefang Deng
Postdoctoral Fellow, SJTU. Research interests: aerodynamic issues in aviation propulsion systems and intelligent design methods.

Xiang Zuo
Ph.D. student (Class of 2025), SJTU. Research interests: generative design of compressors.

Songan Zhang

Tenure-Track Associate Professor at the Global Institute of Future Technology, SJTU, and a member of the Innovation Center of Intelligent Connected Electric Vehicles. Prof. Zhang received the B.S. and M.S. degrees in automotive engineering from Tsinghua University in 2013 and 2016, respectively, and the Ph.D. degree in mechanical engineering from the University of Michigan, USA, in 2021, under the supervision of Prof. Huei Peng, Director of Mcity. Upon graduation, she joined Ford Motor Company as a Researcher and concurrently served as the Committee Chair for the Robotics Proposal Review Panel of the Ford-University of Michigan Joint Program. She has published over 30 papers in journals and conferences, including T-ITS, T-IV, CVPR, and ICCV. Research areas: Decision-making and control algorithms for intelligent vehicles and robotics, reinforcement learning, meta-reinforcement learning, industrial embodied AI, and AI-assisted aircraft engine design.