Numerical analysis of jet-induced vortices in high-head stepped spillways with a PKW crest using the Omega–Liutex method

This study investigates the flow characteristics and energy dissipation mechanisms of a high-head stepped weir equipped with a piano key weir (PKW) crest, focusing on vortex structures along the flume steps. A three-dimensional computational fluid dynamics model was developed in FLOW-3D and validated through grid-independence tests and comparisons with empirical formulas. Subsequently, the validated model was employed to simulate upstream head conditions corresponding to both design and flood scenarios at the Nam Si Luong 3 hydropower plant. To evaluate energy dissipation attributable to vortices, both the classical Q-criterion and the advanced Omega–Liutex method were applied. The results demonstrate that the Omega–Liutex method provides clearer and more physically meaningful identification of coupled vortices, underscoring their significant role in dissipating flow energy along the stepped weir. Compared to the Q-criterion, the Omega–Liutex method reduces false positives in high-shear regions and more accurately captures vortex development, particularly in the skimming flow regime. The findings confirm that integrating a PKW crest with steep steps achieves high discharge capacity while maintaining efficient energy dissipation. This research introduces an Omega–Liutex based vortex analysis approach to improve the understanding of flow behavior in complex spillway systems and provides practical guidance for hydraulic design optimization.