In recent years, the recycling and utilization of low-head river water energy for remote mountainous areas—particularly for water supply, power generation, irrigation, and other livelihood projects—have garnered significant attention. The ultra-low head axial flow hydraulic turbine has become widely adopted due to its ability to operate efficiently under high-flow, low-head conditions. However, the dynamic nature of driving loads, inflow instability, and the presence of multiphase media often lead to speed instability in these turbines. In severe cases, this instability can disrupt the normal operation of the driven load. During model tests of ultra-low head axial flow hydraulic turbines, rotational speed fluctuations under design conditions have been observed to reach up to 20%, resulting in unstable power output. To investigate the underlying causes of this issue, this study focuses on a specific type of ultra-low head axial flow hydraulic turbine and employs the ANSYS Fluent2020R2 dynamic grid SDOF (six-degree-of-freedom) solver for numerical simulations. The research systematically examines the effects of load torque variations, flow rate changes, and gas content on the turbine's rotational speed characteristics. The results show that during startup, the torque coefficient rapidly peaks, undergoes brief fluctuations, and then stabilizes, while the rotational speed sharply increases, experiences minor oscillations, and gradually stabilizes. At steady state, the simulated rotational speed decreases nonlinearly with increasing torque and remains consistently lower than the theoretical speed, with the discrepancy widening at lower torques. This is attributed to higher internal flow velocities at lower torques, increasing frictional losses and reducing recovered power, thereby lowering the rotational speed under constant torque conditions.The turbine's rotational speed closely follows flow rate variations, exhibiting a positive correlation regardless of whether the flow increases linearly or fluctuates sinusoidally. Higher flow rates increase both the turbine head and head loss, resulting in relatively stable efficiency with minor fluctuations and short cycles, indicating uniform efficiency distribution during flow variations. Gas volume fraction significantly impacts performance: increasing it from 0 to 30% reduces rotational speed and power coefficient by 16.4% and 16.2%, respectively, while a rise from 5% to 30% decreases efficiency by approximately 4%. This highlights the detrimental effect of gas content on energy conversion efficiency and operational stability. The study also explores the internal hydraulic losses and efficiency variations under different operating conditions. For instance, during torque fluctuations, the turbine's average efficiency remains around 81%, with water head losses primarily driven by frictional effects. Similarly, flow rate fluctuations lead to efficiency variations of approximately ±10%, which is half the amplitude of the flow rate fluctuations. These insights underscore the importance of maintaining stable inflow conditions and minimizing gas content to ensure optimal turbine performance. The findings of this research provide valuable guidance for the design and operation of ultra-low head axial flow hydraulic turbines. By understanding the relationship between torque, flow rate, gas content, and rotational speed, engineers can develop more effective control strategies to mitigate speed fluctuations and enhance power output stability. This study serves as a foundational reference for future research and practical applications in the field of low-head hydropower systems, particularly in remote and resource-constrained environments.

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.