On the scaling of cavitation inception in tip-leakage vortex flows

The scaling of cavitation inception in tip-leakage vortex flows remains a fundamental challenge in fluid mechanics, primarily due to the complex coupling between macroscopic flow structures and microscopic bubble dynamics. In this study, an Euler–Lagrange framework coupling large eddy simulation with discrete bubble tracking is employed to investigate these scale effects. After validating the model against experimental results, three distinct scale effects are systematically analyzed: velocity scale effect, size scale effect, and the scale effect at the same Reynolds number (Re). The results reveal that the inception cavitation number (σi) exhibits a strong positive correlation with both incoming velocity and size ratio. Even at identical Re, σi increases with the physical size of the hydrofoil, indicating that Reynolds number alone is insufficient to characterize inception scaling. Mechanistically, increasing incoming velocity or size ratio reduces both the time-averaged and fluctuating pressures within the vortex core, while simultaneously increasing the number density of entrained gas nuclei. Crucially, while the macroscopic pressure field maintains spatiotemporal similarity at the same Re, the microscopic gas nuclei distribution varies distinctly with physical scale. Consequently, the conventional velocity and size scale effects are jointly governed by macroscopic pressure variations and microscopic nuclei dynamics, whereas the scale effect at identical Re is fundamentally dictated by the microscopic nuclei transport. These findings provide new insights into the multi-scale physics governing vortex cavitation inception.