Insights into the characteristics of sheet/cloud cavitation and tip-leakage cavitation based on a compressible Euler-Lagrange model

Multiscale structures and fluid compressibility constitute intrinsic features of natural cavitation. However, incorporating these two factors into cavitation simulations remains a formidable challenge. In this work, we propose a compressible Euler-Lagrange method based on the compressible Navier-Stokes equations and a compressible Rayleigh-Plesset (R-P) equation in OpenFOAM. The transient flow field and the Eulerian vapor volumes are calculated with a large eddy simulation approach coupled with a phase transport equation. A bubble motion model along with a compressible R-P equation is solved to predict the trajectory and dynamics of dispersed bubbles. To bridge the macroscopic cavities and microscopic bubbles and consider the bubble-bubble interaction, a four-way coupling algorithm is implemented. The predicted results are validated by comparing with published experiments, and a good agreement is obtained. Further analysis of our results shows that dispersed bubbles will affect the pressure fluctuation characteristics, contributing to more pronounced content in the mid- and high-frequency bands. Additionally, the transient properties of microscopic bubbles will be influenced by the macroscopic cavity with its associated vortex structure. Furthermore, two distinct power laws for bubble size, -4/3 for small bubbles and -10/3 for large bubbles, are obtained. This aligns well with an earlier study [Liu et al., Phys. Fluids 35, 063305 (2023)] and further confirms the reliability of our bubble predictions. This work provides guidance for the setup of bubble size distributions for other numerical algorithms considering the bubble evolution in cavitating flows.