Vortex identification and modal analysis of inter-blade vortices in a pump as turbine under low-flow condition

A centrifugal pump is one of the most important components in a turbine. This study aims to clarify the evolution of the vortex structure in the impeller of a single-stage centrifugal pump. The Omega vortex identification and the dynamic mode decomposition (DMD) were adopted to detect the unsteady flow field under low-flow conditions. The results show that the vortex structure inside the turbine impeller under low-flow conditions was better identified using the Omega vortex identification. The kinetic energy loss was then attributed to the complex flow inside the turbine impeller under low-flow conditions. Specifically, there was the globally large-scale elongated and locally small-scale tubular vortex flow. Multi-scale vortexes were periodically merged, separated, and collided inside the impeller. Furthermore, a more complex flow was observed in the impeller channel under the 0.6Q_d condition. The vortex structure accounted for the most area of the impeller channel. There was an important effect on the performance of the pump as a turbine. The more turbulent vortex was also found in the impeller channel. Many small vortex structures occurred in the flow channel near the impeller outlet. Among them, the fluid first flew into the impeller from the worm shell and then impacted the blade to form a small-scale vortex near the inlet of the impeller channel. The fluid finally flew out into the outlet of the impeller channel; Most regions with the high-flow velocity were distributed in the inlet of the impeller channel near the back of the blade. While the low-flow velocity regions were basically distributed in the middle of the flow channel near the working surface of the blade. Alternatively, the DMD effectively identified the pulsation frequency of the complex flow in the impeller under the low-flow condition. The decomposition was obtained in the first four main modes of the flow field. Their frequency information was divided into the static and dynamic interference, fundamental, and dissipative modes. An outstanding representation was gained for the complex flow in the impeller under the small flow condition. The top four modes were selected, according to the size of the energy modes. At the same time, the one with the highest energy was labeled as the 1st-order mode. The highest energy of the 1st-order mode was 109 750, which accounted for 75.4% of the total energy in the whole flow field. It infers that the 1st-order modes made a great contribution to the whole flow field. The 1st order mode was the static and dynamic interference. The 2nd-order mode with a frequency of 0 represented the basic steady-state structure, in order to characterize the flow field caused by the geometry of the flow channel. The 3rd and 4th order modes were the high harmonic behaviors of the static and dynamic interference. There was the static and dynamic interference effect of the impeller rotating on the flow field. The irregular coherent structure also appeared in the impeller channel in the 3rd and 4th order modes. There were also unstable fluid mass fragmentation and dissipation. The space-time evolution of the unsteady vortex structure was identified inside the pump as a turbine in the region of low-flow condition, indicating the distribution of the coherent structure in each mode. The finding can provide a sound basis to widen the high-efficiency zone of the pump as a turbine.