Source-linked AI summary
A panoramic aerodynamic performance prediction method for turbomachinery cascades using transformer-enhanced neural operator
Qineng Wang, Zhendong Guo, Liming Song, Tianyuan Liu
TL;DR
Turbomachinery design needs faster aerodynamic evaluation because CFD-based downstream analyses require substantial computational effort. The paper introduces a panoramic framework with a Transformer neural operator that predicts basic physical quantities and derives multiple performance outputs. It reports lower prediction error and four-orders-of-magnitude lower downstream optimization cost, while its demonstrated scope is limited to blade-geometry changes.
Problem
CFD-based aerodynamic design tasks require substantial computational effort, motivating faster and reusable prediction alternatives.
Method
The framework predicts basic Navier–Stokes quantities and derives turbine-stage performance parameters, using a Transformer-enhanced neural operator within a reusable panoramic architecture.
Results
TNO reduced the average relative error by 85.5% and reduced multi-objective task optimization cost by 4 orders of magnitude.
Takeaways & Limitations
The framework can reuse one network across multiple downstream tasks while supporting aerodynamic performance prediction in a CFD-like workflow.
Takeaways & Limitations
The study considered only changes in blade geometry, while future work could adjust operating boundary conditions.
Abstract
from arXiv · showhide
To enable flexible and rapid aerodynamic performance evaluation in turbomachinery design, this paper proposes a panoramic performance prediction framework. Unlike most previous prediction models that directly predict the objective functions of interest, our approach first predicts the basic parameters of the Navier-Stokes equations, such as temperature, pressure, and density. Utilizing these basic physical quantities, it subsequently predicts key performance parameters of the turbine stage meridian plane. By adopting this methodology, our proposed panoramic performance prediction framework functions similarly to a CFD simulator, capable of predicting various objective of interest to the designers. To enhance prediction accuracy, a transformer-enhanced neural operator (TNO) is introduced within this framework. Using the Rotor 37 blades as a reference, the proposed TNO is trained to predict the performance of a transonic compressor blade in the meridian plane. The TNO can accurately predict total quantities such as isentropic efficiency, mass flow, and distributions of total pressure ratio. Remarkably, the prediction error of TNO is observed to be smaller than that of state-of-the-art deep learning operators such as the FNO and DeepONet. Furthermore, the TNO is applied to downstream tasks, including sensitivity analysis and optimization of various objective functions. The results confirm that the TNO can operate almost like a CFD simulator, while reducing the computational cost of downstream tasks by four orders of magnitude. The effectiveness and reliability of the proposed TNO for solving different kinds of downstream tasks have been well demonstrated.
1. Introduction
CFD offers accurate turbomachinery analysis but its computational cost complicates time- and budget-constrained design optimization. The paper proposes a reusable panoramic framework that predicts basic physical fields before deriving performance parameters for varied downstream tasks.
- The framework targets turbomachinery design optimization, where increasing CFD accuracy also increases per-run cost and makes optimization difficult within practical time and budget constraints.
- Conventional surrogate models improve design efficiency but neglect rich CFD flow-field data, limiting interpretability and producing black-box predictions.
- Deep-learning flow-field predictors can produce results within milliseconds and substitute CFD in certain scenarios, but their datasets and training are costly when restricted to one field and computational domain.
- The proposed panoramic framework predicts basic Navier–Stokes quantities, including temperature, pressure, density, and velocity, then derives turbine-stage meridian-plane performance parameters.
- A Transformer-enhanced neural operator is integrated to improve prediction accuracy, with Galerkin attention identified as its operator mechanism.
- Applied to Rotor 37 transonic-compressor aerodynamic design, the framework supports varied downstream tasks and demonstrates flexibility, reusability, and reduced task time.
2. Problem Setup and Data Preparation
The study parameterizes Rotor 37 blade geometries, evaluates them with validated CFD, and prepares paired design-variable and flow-field data for panoramic prediction. Its workflow then trains and assesses a network for flow-field and performance prediction and downstream tasks.
- 2.3. Data preparation: 2900 Latin-hypercube samples span 28 geometric design variables, with each case pairing design variables x and Rotor 37 flow fields f.These paired data cases are used to train and validate deep operator networks.
- 2.3. Data preparation: The workflow prepares training data, establishes a panoramic performance-prediction network, evaluates flow-field and performance accuracy, and supports downstream-task assessment.The developed network is intended for near-real-time prediction of flow fields and performance metrics for specific blade geometries.
3. Proposed Method
The paper builds a panoramic turbomachinery prediction framework that predicts basic physical fields before deriving performance quantities. Its Transformer Neural Operator combines branch-trunk operator structure with Galerkin attention for efficient multi-field prediction.
- Transformer Neural Operator: TNO is designed to predict multiple physical fields governed by the Navier-Stokes equations.The selected basic fields include pressure, static temperature, absolute velocity, relative velocity, and mass flow rate.
- Panoramic prediction framework: The framework predicts basic physical fields from design variables and derives performance parameters for downstream tasks.It is organized into a network structure, panoramic predictor, and downstream task components.
- Transformer Neural Operator: The TNO uses a branch-trunk operator architecture that encodes design variables and query locations before combining their features.The branch network encodes design variables, while the trunk network processes meridian-plane query locations.
- Transformer Neural Operator: Galerkin attention replaces vanilla attention, simplifying softmax computation to enhance calculation speed.The trunk network uses multiple Galerkin attention blocks and feed-forward networks.
- Transformer Neural Operator: The shared output network transforms combined branch and trunk features to process multiple physical fields simultaneously.The architecture applies geometric information globally through feature operations before producing the output fields.
- Panoramic performance calculation: The framework computes averaged flow quantities through circumferential and spanwise integration, then derives performance metrics from the predicted fields.The meridian-plane representation uses weighted integration of the five basic fields before performance calculation.
4. Results and discussion
The experiments evaluate TNO against several neural networks for Rotor 37 flow-field and performance prediction. TNO achieves the strongest reported accuracy, accelerates prediction and optimization, and supports sensitivity analysis through panoramic flow-field information.
- Efficiency: 0.9 ms was TNO’s approximate prediction time, five orders of magnitude lower than CFD simulation time.The comparison covers model size, memory, training, and flow-field prediction time for five networks.
- Basic-field prediction: 85.5% average error reduction versus FNO made TNO the most accurate network for the five basic physical fields.The paper reports that TNO achieved the highest prediction accuracy among the compared networks.
- Flow-field validation: TNO accurately reproduced all five basic physical fields and maintained high accuracy for derived fields in the valid-A case.The validation comparison is presented in Figures 8 and 9.
- Performance prediction: TNO best predicted Rotor 37 efficiency, pressure ratio, and mass flow, while the networks reproduced overall spanwise performance trends.For the worst TNO case, valid-D, efficiency was overpredicted.
- Overall performance comparison: 12 of 15 metric–sample-size scenarios had the lowest prediction error with TNO, including every scenario using at least 1500 training samples.This comparison is reported across the scenarios in Table 8.
5. Conclusions
The paper presents a panoramic turbomachinery prediction framework centered on TNO, which predicts basic physical fields and derives reusable performance parameters for downstream design tasks. Tested on Rotor 37, it reports faster and more accurate prediction than comparison models, with four-order-of-magnitude efficiency gains in optimization, while currently varying only blade geometry.
- Motivation: The framework targets flexible and rapid aerodynamic performance evaluation for turbomachinery design, a key aerospace design challenge.Its stated purpose is to expedite downstream aerodynamic design tasks.
- Framework and method: TNO predicts Navier–Stokes basic physical fields, enabling derived performance parameters and reuse across multiple downstream tasks.The framework uses predicted basic fields to compute desired performance quantities rather than directly predicting each objective.
- Results: TNO inference takes approximately 0.9ms, reducing prediction time relative to CFD and existing models.The conclusion describes the neural-operator inference as much faster than the CFD numerical method.
- Results: 85.5% lower average relative error than FNO networks demonstrates improved prediction accuracy on the Rotor 37 transonic compressor case.The framework is evaluated using the Rotor 37 blade as a representative turbomachinery test case.
- Limitations and future work: The study varies only blade geometry; future work will include operating boundary conditions and active learning to reduce training samples.These extensions aim to cover more turbomachinery design scenarios and focus data on critical regions.
6. Appendix
The appendix documents grid-independence verification, comparison-network structures, and predicted-versus-CFD field visualizations for validation cases.
- Validation: Figure 18 presents grid-independence verification, with the black box marking the selected grid.
- Comparison models: Tables 11–14 document the detailed network structures of MLP, UNet, deepONet Branch Network, and FNO.
- Network specification: The reported network specification includes an input size of 4096×2, ten Linear + GELU blocks, and output size 4096×5.
- Network specification: The listed forward-pass size is 822.56MB and the parameter size is 1.79MB.
- Validation: Figures 19 and 20 compare predicted, CFD, and error maps for basic and derived fields in valid-B and valid-C.Figure 19 covers basic fields, while Figure 20 covers derived fields.