Unraveling Coherent Structures in Pump-Turbine Tandem Cascades Using Enhanced SPOD

Abstract In high-speed reversible pump-turbines, tandem cascade flow instability under off-design low-flow (LF) conditions severely restricts the performance of pumped storage units, leading to efficiency loss, vibration amplification, and reduced operational longevity. However, the spatiotemporal coherent structures associated with this instability remain poorly characterized. To further reveal the near-vane flow instability, a modal decoupling technology-based flow feature extraction approach is explored, combining spectral proper orthogonal decomposition (SPOD) with an in-house hyperparameter optimization (IHO). SPOD extracts spatial features of tandem cascade flow by decoupling statistically stationary flows into frequency-resolved and energy-ranked modes, while IHO determines the optimal spectral estimation parameters. The time-resolved data used for the SPOD analysis are obtained via high-fidelity computational fluid dynamics (CFD) simulation tailored for tandem cascades, validated against the experimental data from a power station. Two case studies are analyzed for comparison. For the off-design low-flow condition, modal analysis from SPOD–IHO shows that most energy comes from the main mode at the edge of the runner and the stay vane, both of which are low-frequency and low-rank. For the rated flow (RF) condition, the most energy comes from the main mode only at the edge of the runner. We later evaluated the proposed SPOD–IHO method against baseline SPOD, and the proposed SPOD–IHO exhibits a more refined and physically coherent vortex roll-up structure. These findings have significant implications for guiding designers to efficiently extract dominant flow features and target key regions associated with hydrodynamic instability in tandem cascade flow. Some of the highlights are as follows: (1) an IHO for spectral estimation parameter selection, (2) a CFD model tailored for tandem cascades under off-design low-flow conditions, (3) modal visualization analysis of tandem cascades flow field under off-design low-flow conditions, and (4) a comparative study of the proposed SPOD–IHO method with baseline SPOD approaches.