A Rortex-based method for evaluating hydraulic losses in pump-turbines: a case study of turbine mode under different load conditions

When pump-turbines operate under off-design conditions, complex internal vortex flows often arise, leading to hydraulic instabilities and increased energy losses. Traditional hydraulic loss evaluation methods fail to quantitatively link vortex structures to energy dissipation mechanisms, limiting their ability to guide design improvements. To address this gap, this study proposes a Rortex-enhanced hydraulic loss evaluation framework to systematically analyze vortex dynamics and associated energy dissipation across wide-load turbine-mode operating conditions. By decomposing the dissipation terms in the mean turbulent kinetic energy equation, the framework identifies rigid vorticity-induced dissipation, shear vorticity-induced dissipation, and rotational-shear coupling losses. Numerical simulations, validated by experimental data, show that shear vorticity-induced dissipation dominates overall hydraulic losses, primarily along blade surfaces and boundary layers. Although rigid vorticity-induced dissipation contributes less overall, it increases significantly at lower loads and is concentrated around vortex peripheries due to shear interactions. Energy losses within vortex cores are predominantly driven by rotational-shear coupling effects, strongly correlated with the enstrophy of the pseudo Lamb vector curl term (ERCT). These findings suggest that suppressing ERCT-driven vortex formation and mitigating rotational-shear interactions through optimized blade designs could effectively reduce energy losses and enhance the hydraulic stability and efficiency of pump-turbines.