Negative phase gradient-based analysis of energy evolution characteristics of low-dimensional coherent structures in oscillating water column under part-load condition

As core components of oscillating water column wave energy converters, air turbines are susceptible to intense unsteady flows and complex pressure pulsations under part-load condition. Although standard dynamic mode decomposition can identify characteristic frequencies and spatial structures, its interpretation does not directly provide full-field evolution pathways and origin information for coherent structures. To address this, a Negative Phase Gradient-Based Low-Dimensional Coherent Structure Evolution (NPG-LCE) analysis method is proposed to investigate the spatiotemporal evolution mechanisms of multi-scale pressure pulsations in an air turbine. Based on a simplified two-dimensional turbine model, low-order modes are extracted from numerical simulations validated by experimental data, and the internal flow under part-load condition is analyzed. The phase and spatial gradient characteristics of key modes are quantified, and the spatiotemporal evolution pathways of the pressure pulsations are identified. Results indicate that, besides conventional rotor-stator interaction frequencies, the pressure field is dominated by two atypical low-frequency pulsations: f VBR (56.67 Hz), associated with vane-blade ratio interaction, and f SVE (10 Hz), associated with the evolution of separation-related flow structures extending away from blade surfaces. The proposed method extends standard DMD by providing a spatiotemporal evolution interpretation of coherent structures, facilitating the analysis of complex unsteady flow evolution patterns in turbomachinery.