Development of a compressible multi-scale model for cavitating flows*

A compressible multi-scale model is developed to accurately predict the dynamics of both the resolved vapor and the sub-grid bubbles during cavitation inception. Here, the mixture of liquid and resolved vapor is treated as a carrier fluid and the sub-grid bubbles are tracked in a Lagrangian sense by the Rayleigh-Plesset equation. Also, a mixture equation of state is used that accounts for the compressibility of the mixture medium. The differences between the proposed model and the homogeneous mixture model are discussed. A modified Rayleigh-Plesset equation, which can better predict the bubble behavior in the presence of a large number of bubbles, is presented and compared to the traditional Rayleigh-Plesset equation. This model is then applied to complex cases (O(10^3) sub-grid bubbles) where phenomena such as violent bubble collapse, shielding effects etc. are observed.