The vortex dynamics characteristics in a pump-turbine: A rigid vorticity analysis while varying guide vane openings in turbine mode

In off-design conditions, pump-turbines generate vortex structures of varying scales and intensities, jeopardizing energy conversion due to unstable flow phenomena. While off-design pump-turbine internal flow dynamics have been analyzed, understanding the spatiotemporal evolution of complex vortex structures within runner blade passages, which are prone to inducing hydraulic instabilities, has to be still addressed properly. This paper applies the rigid vorticity theory, also known as Liutex, to explore vortex characteristics in the pump-turbine under different guide vane openings during turbine mode operation. The investigation focuses on three main aspects: i) spatial distribution characteristics, ii) temporal evolution characteristics, and iii) vortex morphological features along with deformation mechanisms. Results showed that the suction surface side of the blade's trailing edge commonly experiences significant shear effects, while vortices tend to emerge on both pressure and suction surface sides. Under small Guide Vane Opening (GVO) condition, vortices in blade passages show periodic evolution, and Enstrophy of the Rigid Vorticity Dilatation Term (ERDT) predominantly contributes to the helical deformation of these vortices. Conversely, under large GVO condition, vortices maintain high helicity and remain stable. This study provides insights to reduce hydraulic instability in pump-turbines and optimize energy conversion efficiency. The proposed Reynolds-averaged transport equation for enstrophy of the rigid vorticity and the relative streamline coordinate system provide advanced tools for analyzing unstable flow structures.