Prediction model of the three-dimensional flow field in compressor cascades using shallow neural networks based on sparse pressure data

Real-time prediction of the internal three-dimensional (3D) flow field serves as a key enabler for developing advanced closed-loop flow control systems in compressor components of aircraft engines. To this end, this study develops a data-driven prediction framework based on a shallow neural network architecture, leveraging the physical correlation between the wall pressure field and the complex 3D internal flow field. The model predicts the total pressure distribution at the cascade outlet from only 13 sparse measurements on the upstream blade and end wall, with optimal sensor locations are determined using the leverage score sampling method. The model's generalization and stability are systematically evaluated through sevenfold cross-validation and extrapolation tests. The results demonstrate acceptable predictive fidelity, with over 97.3% of test cases achieving a Pearson correlation coefficient above 0.85 against computational fluid dynamics data, at millisecond-level prediction speeds. This level of performance is achieved using less than 2% of the measurement points required by traditional experimental setups. Further analysis reveals that the complex corner separation flow within the passage is the main source of prediction error. Collectively, these findings establish this work as a real-time prediction framework that achieves a favorable balance between prediction speed and accuracy, meeting the sensing demands of advanced closed-loop control.