Abstract
Accurate reconstruction of unsteady flow fields in turbomachinery is essential for aerodynamic optimization and condition monitoring in energy and propulsion systems, but time-resolved measurements are frequently limited by hardware sampling capability and by basis mismatch under variable operating conditions. This study proposes a multi-condition joint sparse reconstruction framework that integrates cross-domain data assimilation, a weighted cross-correlation criterion, and mixed l2,1-norm optimization. A universal joint POD basis is developed from flow-field correlations among different incidence angles to improve cross-condition representation, while the row-sparse coefficient formulation exploits shared coherent structures across operating states. The method is validated using time-resolved PIV data from a compressor cascade at five incidence angles from 0° to 10°. Results show that the proposed POD-based joint reconstruction markedly outperforms conventional reconstruction methods. At a compression ratio of 0.6, the mean squared error is reduced by about 89.6% compared with the conventional POD-based approach. For the five-condition envelope, the weighted joint basis captures common structures across incidence states, although larger errors occur at high incidence due to stronger separation and condition-specific vortical dynamics. The method remains robust to different sampling-frequency combinations once the compression ratio exceeds the information threshold. The proposed framework provides an effective physics-informed data assimilation strategy for high-fidelity unsteady flow-field reconstruction under sparse sampling and variable operating conditions.