Unveiling the characteristics of bubble dynamics and accompanied released energy for a cavitating Clark-Y hydrofoil by a bubble-cluster approach

A one-way coupled Eulerian–Lagrangian computational framework integrating the homogeneous flow theory and discrete phase model was developed to investigate the hydrodynamic characteristics of sheet cavitation, cloud cavitation, and supercavitation, as well as the mechanism of released energy in cavitation. Numerical simulations were conducted for a Clark-Y hydrofoil at three typical cavitation numbers (σ = 0.4, 0.8, and 1.4). An energy assessment model that incorporates bubble–bubble coalescence effects was developed and coupled with the Gilmore-Noble-Abel-stiffened-gas equation to obtain the bubble dynamics. The findings indicate that the bubble radius and internal pressure variations exhibit a positive correlation with the intensity of flow field pressure. Under the most unstable cloud cavitation conditions (σ = 0.8), cavitation bubbles located in the high-fluctuation flow field region exhibit large internal pressure amplitudes, with peak potential and kinetic energy reaching 0.018 and 0.016 mJ, respectively. Simultaneously, these bubbles collapse through multiple distinct manners. The maximum potential energy of the cluster in this region is 12.31 mJ, and the overall released and converted flow field kinetic energy is 11.03 mJ. The bubble potential energy reaches its maximum when the bubble radius is at its peak, while the flow kinetic energy approaches to zero. Variations in the initial bubble radii not only alter the bubble surface tension but also govern the coalescence probability among neighboring bubbles. The methodology developed in this study provides a theoretical guidance for the investigation of energy characteristics induced by bubble dynamic evolution in cavitation flows for large-scale hydraulic machineries.