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This study aims to elucidate the rotor–stator interaction (RSI) mechanism in a centrifugal pump by employing high-fidelity stress-blended eddy simulation (SBES) turbulence modeling combined with reduced-order techniques [dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD)]. The core objective extends beyond confirming the dominant frequency characteristics, to quantifying the energy hierarchy of RSI-induced flow and resolving the energy cascade in a coupled space–time–frequency domain. The present work investigates the RSI in a pump based on the European Research Community on Flow, Turbulence and Combustion standard through three-dimensional, unsteady computational fluid dynamics simulations. Initially, the SBES and scale-adaptive simulation turbulence models were compared. It was observed that the SBES model had good predictive accuracy compared to the experimental data for the pressure coefficient, velocity profiles, and pressure fluctuations in the vaneless region. Further transient study using SBES showed that blade passing frequency (fBPF) and its second harmonic are the predominant frequencies in terms of pressure pulsations. Also, the energy variability of frequencies was distinct across the flow path. Reduced-order analysis showed low-dimensional features of the flow. DMD's isolation of the first four dominant modes, corresponding to fBPF and its harmonics, was successful, with their spatial structures visualizing the large-scale periodic wakes and associated small-scale vortex shedding from RSI. A reconstruction based only on the first 5 DMD modes is able to capture the essential dynamics of the actual flow field in the study. POD analysis confirmed previous results for the energetic behavior. It clearly indicates that the first four modes contain more than 66% of the total energy. Moreover, the corresponding spectra of modal coefficients perfectly align with the DMD frequencies. This synergy of results confirms that periodic wakes from RSI are the primary energy-driving mechanism. This work seeks to reveal how the transient vortex structures influence pressure and Reynolds stress fluctuations, thereby providing physical insights beyond conventional spectral analysis for flow-induced vibration and noise control, and offers a basis for optimizing fluid machinery design.