Energy distribution and chaotic pressure pulsation analysis of vortex ropes in Francis-99

Abstract

Francis turbines, essential for stability in diverse operating conditions and variable-speed scenarios, encounter efficiency-compromising vortex rope formations in the draft tube, leading to substantial pressure fluctuations. This research delves into the analysis of energy loss and pressure fluctuations associated with these vortex ropes. Employing the local entropy generation rate (LEGR) method and chaos theory, we scrutinize the behaviour of vortex ropes and their resultant pressure fluctuations. Notably, vortex ropes exhibit maximum LEGR near the runner cone, with secondary vortices escalating instability downstream. In the elbow section, the collision of vortex ropes with the outer elbow amplifies LEGR, primarily driven by fluctuating velocities (approximately 90%). Leveraging the GWO-VMD algorithm, non-stationary signals are decomposed, unveiling a significant 1.6 Hz vortex rope frequency under partial load (PL) conditions and isolating external noise frequencies, such as the prominent 300 Hz. Following decomposition, chaos theory tools, including phase space reconstruction and phase trajectory graphs, unveil the chaotic nature of PL conditions attributed to spiral vortex ropes, resulting in profound pressure fluctuations. This study enhances our understanding of such systems and provides methodologies for improved noise reduction and optimization of turbine performance.