Data-Driven Sparse Reconstruction of Three-Dimensional Steady and Unsteady Flow Fields in a Centrifugal Impeller

Abstract This study evaluates the reconstruction of three-dimensional steady and unsteady flow fields in a centrifugal impeller using proper orthogonal decomposition (POD) and sparse sensing techniques. This approach is driven by the fundamental challenges in turbomachinery, where spatial and instrumentation limitations greatly restrict the range of measurable physical quantities. Using POD, this study seeks to efficiently extract the dominant flow structures, enabling their accurate reconstruction even from sparse sensor data. For time-averaged flow, the first two POD modes account for 99.4% of the energy, capturing deviations from the design flow rate and localized variations in secondary flow. Optimal sensor placement algorithms, i.e., determinant-based greedy (DG) and Bayesian determinant-based greedy (BDG) methods, achieved accurate flow field estimation with a minimal number of sensors. For time-varying flow, the first two modes capture the interaction between the blade and tongue, and the third and fourth modes represent higher-order harmonics of the first and second modes. The BDG method outperformed others in selecting sensor locations, leading to smaller estimation errors in both velocity and pressure fields. Incorporating Bayesian estimation into the reconstruction process further enhances robustness, ensuring reliable results even in the presence of noise. This research provides a deeper understanding of flow dynamics, even with limited measurement data, and holds the potential for controlling and optimizing turbomachinery in practical applications such as real-time monitoring, anomaly detection, and feedback control systems.