A panoramic aerodynamic performance prediction method for turbomachinery cascades using transformer-enhanced neural operator

Accurate prediction of unsteady aerodynamic loads remains a major challenge in turbomachinery design. High-fidelity Computational Fluid Dynamics (CFD) simulations are expensive, while aeroelastic Quantities of Interest (QoI) depend sensitively on the temporal evolution of the pressure field. This work introduces periodic Fourier Neural Mapping (p-FNM), a neural-operator framework for predicting unsteady pressure distributions on turbine rotor blades simulated using the chorochronic numerical hypothesis. The architecture embeds temporal periodicity into the model and learns a continuous mapping from operating conditions and time to pressure fields. Unlike sequential latent-space approaches, p-FNM predicts pressure fields independently at any time, avoiding error accumulation while preserving temporal continuity. The model is evaluated on a database of unsteady rotor-blade simulations and compared with a reduced-order baseline based on a variational autoencoder and recurrent neural network, refered as the Temporal Prediction Model (TPM). Performance is assessed for pressure fields and Generalized Aerodynamic Forces (GAFs), the primary aeroelastic QoI. Across all training datasets, p-FNM consistently outperforms TPM. On the largest dataset, p-FNM achieves a pressure-field mean absolute percentage error of 0.46% and a GAF-magnitude prediction error of 4.42%, corresponding to improvements of 60.7% and 77.6%, respectively. The minimum weighted phase error reaches 0.060 rad, demonstrating accurate preservation of the temporal characteristics of the aerodynamic response. The results show that GAF prediction is more challenging than pressure-field prediction and that temporal coherence is critical for accurately predicting spectral aerodynamic quantities. These findings demonstrate the potential of periodic neural operators for reduced-order modeling and aeroelastic analysis in turbomachinery.

In this study, a physics-enhanced neural operator framework is proposed to enhance the generalization prediction ability of the cooling layout of a turbine endwall with variable number of film holes. Specifically, inspired by the film cooling superposition principle, we propose a film cooling prediction model, namely superposition-based deep neural operator (SDNO), that divides the endwall temperature field prediction into two stages. In the first stage, the cooling layout of a turbine endwall is divided into several sub-parts with randomly assigned film holes, and a Transformer-based neural operator network, namely Calculate Net, is designed to predict the temperature field of each sub-part. Then, in the second stage, another neural operator network, i.e., Super Net, is trained to combine the temperature fields predicted by Calculate Net for each sub-part and obtain the superposed temperature field of the full cooling layout. Additionally, instead of directly taking the film cooling contours as pixel plots, a signed distance function (SDF) which is sensitive to the variable locations of cooling holes, is designed to encode the location information of cooling holes. Furthermore, the proposed endwall film cooling prediction model is trained with the samples that changing the number of film holes from 1-5 with variable locations. Then, the trained prediction shows excellent generalization prediction ability, which can accurately predict the film effectiveness of the cooling layout with 10-20 film cooling holes that are unseen in the training samples. The proposed SDNO also improves prediction accuracy relative to the fully supervised baseline. With the above, the effectiveness of our proposed prediction model has been well demonstrated.

Neural operators offer an efficient data-driven approach to rapid prediction of complex automotive aerodynamic flows. However, spectral bias and other factors limit accurate reconstruction of fine-scale flow variations near complex geometries. Existing studies improve the representation and fitting of fine-scale information mainly through information extraction and training objectives. Further study is needed to determine how extracted local details can be used continually in subsequent operator computations and contribute effectively to the overall flow-field representation. We propose CIS-Transolver, a cross-layer incremental-state neural operator that extends fine-scale modeling from local information extraction to its use across layers. The method extracts fine-scale information through local multiscale analysis and encodes it as geometric moment states that are propagated and updated across layers. By combining information from previous layers with feedback to the value representations in Physics-Attention, the method allows local details to contribute continually to subsequent modeling of global physical correlations. We systematically evaluate CIS-Transolver on three public automotive aerodynamics benchmarks, ShapeNet-Car, AhmedML, and DrivAerNet++, covering surface pressure fields and volumetric pressure and velocity fields. CIS-Transolver achieves the lowest mean relative L2 error among the evaluated methods for all five prediction metrics across the three benchmarks. The relative error reductions average 8.72% across the five metrics compared with the best baseline for each metric, reaching 16.38% for ShapeNet-Car pressure prediction and 15.60% for AhmedML velocity prediction. These results provide a new approach to fine-scale flow prediction for complex geometries.