Application of Proper Orthogonal Decomposition in Spatiotemporal Characterization and Reduced-Order Modeling of Rotor–Stator Interaction Flow Field

The periodic unsteady flow induced by rotor–stator interaction (RSI) is the primary cause of blade forced vibration and fatigue failure. Therefore, analyzing the excitation characteristics of RSI flow fields under multi-parameter conditions is essential for vibration analysis and optimization in fluid–structure interaction. This study derives the Toeplitz structure of the correlation matrix in proper orthogonal decomposition (POD) for strictly periodic flow fields and reveals that the POD spatial modes appear in pairs with a 90° spatial phase difference, which originates from the cosine and sine form of the eigenvectors of the Toeplitz matrix. Taking a 1.5-stage compressor cascade as an example, the POD method is employed to effectively extract the main spatiotemporal characteristics of the RSI flow field, and the spatial symmetry and phase difference of the POD modes are further interpreted from a physical perspective. To address the high computational cost and resource demands arising from large-scale similar cases in multi-parameter excitation optimization and analysis, a reduced-order modeling (ROM) method based on time–space and parameter decoupling is proposed using multi-parameter POD. Spatial bases are extracted through the first-level POD, and a second-level POD is applied to the first-level coefficients to obtain temporal bases and coefficients that are solely parameter-dependent. A radial basis function (RBF) interpolation is used to establish the mapping between parameters and the second-level coefficients, enabling efficient multi-parameter ROM construction. The resulting ROM achieves a relative prediction error of less than 1.4% under typical operating conditions and less than 2.9% near the choke boundary, improving computational efficiency by four orders of magnitude while maintaining accuracy, thereby providing an effective approach for aerodynamic excitation acquisition.