A new cavitation model based on bubble-bubble interactions

Abstract

In this paper, a new model based on bubble-bubble interactions is proposed for cavitation. Unlike the well-known existing models (Rayleigh-Plesset, Gilmore), which are derived from the local balance equations in the vicinity of a single cavitation bubble, the present approach is based on the mutual interaction between two spherical bubbles of different sizes. The mass and momentum conservation equations, coupled with the local flowdivergence, lead to two equations for the evolution of the bubble radii and one equation for the local pressure. The bubble size variations predicted by the model are found in close agreement with the previous experimental data reported by Ohl [“Cavitation inception following shock wave passage,” Phys. Fluids 14(10), 3512–3521 (2002)]. The distinct radii of bubbles located close to each other, as well as the premature collapse of small bubbles during the initial stage of cavitation inception, are correctly reproduced by the model. The results generally show that bubble/bubble interactions play a primary role in the physics of cavitation inception, which is a preponderant phenomenon in cavitation-induced noise and erosion. The influence of the size of the nuclei on these interactions is discussed. During the expansion phases, the variations in the local flow divergence only slightly affect the growth of the big nuclei, which is mainly governed by their interaction with the neighboring bubbles, while it triggers the expansion of the small nuclei. Conversely, in the compression phase, the behavior of the bubbles is not influenced anymore by the initial size of the nuclei. It is also shown that large amplitude pressure variations resulting from the multiple collapses of small bubbles should be taken into account, in addition to the ambient pressure evolution, to calculate the instantaneous local pressure in the liquid and eventually evaluate the flow aggressiveness and the resulting erosion.