A fully compressible multi-scale model for cavitating flows

A key feature of cavitating flows is the presence of vapor over a wide range of length scales. A compressible multi-scale model that captures (a) massive vapor cavities and sub-grid bubble dynamics, (b) compressibility of the mixture medium and (c) inter-bubble interactions is developed. The homogeneous mixture of liquid and resolved vapor is tracked in an Eulerian sense and the sub-grid bubbles are tracked in a Lagrangian sense using a novel RP variant termed the ‘generalized RP equation’. Integrating the spherical momentum equation to a finite distance kR (k is a constant parameter) and combining it with the linear wave equation yields the generalized RP equation. Such an approach results in p(kR) (pressure at a finite distance from the bubble) being the external rather than p∞(pressure at infinite distance). This allows for the inter-bubble interactions to be captured via p(kR). The multi-scale model is first validated for a single resolved/unresolved bubble. Its ability to capture the inter-bubble interactions for sub-grid bubbles and the interaction between a resolved vapor cavity and an unresolved bubble are also demonstrated. It is applied to a bubble cloud exposed to a strong acoustic pulse where phenomena such as violent bubble collapse, shielding effects etc. are observed.