Abstract: Spiral vortex ropes in the draft tube under certain partial load conditions could be frequently observed in the model tests of Francis turbines. In addition to typical vortex rope rotation frequencies fv, pressure signals recorded at the draft tube wall monitor points often exhibit the rotational frequency fn and its higher-order harmonics (1 ~ 5)fn as distinct spectral components. Under certain operating conditions, these special frequency components show significant amplitudes, yet their underlying generation mechanisms remain controversial. This study examines the internal flow characteristics of a Francis turbine operating under typical vortex rope conditions. By combining the data from high-speed imaging with pressure fluctuation measurements, this study presents a systematic analysis on the effects of unit discharge, unit speed, and cavitation number on the vortex rope structure and pressure pulsation characteristics, focusing on analyzing the possible sources of the harmonics (1 ~ 5)fn. The results indicate that unit discharge significantly influences the amplitude of the vortex rope rotation at fv when the spiral vortex rope is visible, pressure pulsation amplitudes at fv increase substantially. In contrast, weaker effects of cavitation number and unit speed are cast on the amplitude at fv. Additionally, under certain specific conditions, a slender and stable cavitating spiral vortex rope forms in the draft tube, where the amplitude at fn sharply increases. This phenomenon is believed to be closely related to hydraulic system resonance triggered by this cavitating rope. The special harmonics at (1 ~ 5)fn are likely attributed to the elliptical cross-section of the vortex rope and its self-rotation, which is characterized by frequencies close to (1 ~ 5)fn.

Key words: Francis turbine, pressure pulsation test, cavitation, vortex frequency, rotational frequency