Mechanism of energy dissipation in cavitation vortices of low head axial flow pump-as-turbine via reduced-order variational mode decomposition

When the low head pump-as-turbine (PAT) mode, the nonlinear coupling of vortex systems (namely draft-tube and blade–passage vortices) and the intensification of cavitation degrade both efficiency and operational stability. Existing signal–decomposition techniques (e.g. EMD, EWT) struggle to disentangle these interacting vortex modes and their associated energy–dissipation mechanisms. To overcome these limitations, this study fuses reduced-order variational mode decomposition (RVMD) with entropy–production theory. By imposing physics–based constraints, RVMD achieves high–fidelity separation of multimodal phenomena (such as cavitation vortices), while avoiding mode mixing. Each extracted mode is then embedded within an entropy–production framework to establish a quantitative mapping between specific vortex dynamics and local energy–dissipation rates. Cavitation severity is characterized by the dimensionless Thoma number σ (smaller σ indicates more severe cavitation). Our results reveal two regimes: The head is 4.4 m. Initial cavitation stage (σ = 0.831): Energy concentrates predominantly in mid–frequency modes (Modes 3 and 4), accounting for 62% of the total, with minimal instability. Severe cavitation stage (σ = 0.388): Cavitation vortices dominate low–frequency modes (Modes 1 and 2), comprising 78% of the signal. The overall dissipation rate surges to 24.7%, with low–frequency modes contributing 71% of the additional loss under strong cavitation. The proposed ‘high–precision modal separation to mode–specific entropy–production evaluation’ framework addresses a critical bottleneck in deciphering complex vortex dissipation mechanisms. It offers a broadly applicable tool for energy–optimization in turbomachinery and other systems with intricate flow dynamics.