Influence of Bézier curve based variable-speed control strategies on transient flow characteristics in pump-turbine under pump mode: A combined vortex dynamics and rothalpy analysis

This study systematically investigates the influence mechanisms of different Bézier curve-based variable-speed control strategies on the internal flow characteristics of a pump-turbine (PT) operating in pump mode. The analysis integrates the Omega vortex identification method, rothalpy change theory, and a time-frequency analysis approach utilizing the Frequency Slice Wavelet Transform (FSWT). A combined methodology of a full-flow-passage visualization experimental platform and high-fidelity Computational Fluid Dynamics (CFD) simulations is employed to elucidate the evolution of vortex structures and their intrinsic correlation with pressure pulsations during transient speed change processes. The results demonstrate that, compared to a linear Bézier strategy, the quadratic Bézier curve-based strategy exhibits superior performance. In terms of external characteristics, this strategy facilitates a smoother power transition, significantly reducing power oscillation amplitude by approximately 16.3%, effectively mitigating hydraulic impact and enhancing system operational stability. Regarding internal flow mechanisms, the Omega method accurately captures the spatiotemporal evolution of vortex cores during the speed transients. Under quadratic regulation, vortex structure development within the double-row cascade and runner passages is more orderly, with a final overall reduction of about 51.57% at steady state. High-value regions of turbulent frequency are concentrated in specific areas, indicating an excellent suppressive effect on small-scale turbulent fluctuations and flow separation. Rothalpy analysis further reveals that the quadratic Bézier curve, through its non-linear acceleration characteristics, promotes a more uniform distribution of rothalpy gradients and a marked reduction in high-value regions. This effectively regulates secondary flows driven by rothalpy change and suppresses the generation of disordered vortices. Furthermore, pressure pulsation analysis indicates that the quadratic Bézier curve significantly reduces pulsation amplitudes across multiple blade height (mid-span) sections, with more stable time-domain characteristics, ensuring low-vibration and high-reliability unit operation. Time-frequency domain analysis further shows that under quadratic Bézier regulation, pressure pulsation energy is more concentrated in the time-frequency domain, high-frequency components are significantly suppressed, and pulsation amplitudes are reduced, demonstrating superior transient flow stability. This research deepens the understanding of internal flow control in variable-speed pump-turbines and provides a significant theoretical basis and strategic support for the optimal design and stable, efficient operation of variable-speed units.