Coherent structure analysis of double-helix vortex rope in pump turbine operating in turbine mode based on POD and DMD

Under low-part load conditions, Double-helix Vortex Rope (DVR) can occur in the draft tube of pump turbines, causing pressure pulsations that contribute significantly to the instability of Pumped Storage Power Stations (PSPS). With the intent of studying the characteristics of the DVR in draft tube, this paper focuses on a model pump turbine that operated stably at 43 % low-part load. Systematic numerical calculations were conducted, extracting 600 snapshots of the flow field from longitude slice of the draft tube during last 5 runner revolutions to form a pressure matrix for Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The results show that the pressure pulsation induced by DVR (f_DVR) is 0.8 f_n, which is approximately twice the traditional Single-helix Vortex Rope (SVR). POD analysis revealed that the dominant frequency of the POD mode 1 and 2 are both f_DVR and the summation energy contributions of them exceeded 70 %. However, frequency aliasing existed in each POD modes. In contrast, DMD analysis showed that the frequency of the DMD mode 3 with 1 % energy contribution is 0.85 f_n, which is closed to the f_DVR, and no frequency aliasing existed. POD modes 1, 2, and 5, along with all DMD modes except mode 5, significantly impact the flow field. Pressure contour of the DMD mode 3 is similar to the POD mode 1 and 2, suggesting a link to the DVR. Additionally, the time evolution of DMD mode 3, extracted at different moments, reveals that it characterizes the spinning process of the DVR. This study provides new insights to the DVR and offers a reference for achieving more stable PSPS operation.