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 flow divergence, 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.
Highlights
In this paper, a new model based on bubble-bubble interactions is proposed for cavitation
The microscopic air or vapour bubbles contained in the liquid progressively grow and become macroscopic bubbles mainly composed of vapour
The single fluid models— called homogeneous models—treat both phases as a single continuous, homogeneous fluid, with an average density. They are based on the classical balance equations for compressible or pseudo-compressible flows. They can be divided into three groups, according to the closure equation of the problem: (i) the barotropic models use a postulated equation of state that links the density to the pressure (Delannoy and Kueny, 1990; Coutier-Delgosha et al, 2003; and Koop and Hoeijmakers, 2006), (ii) the models based on a transport equation for the volume fraction of vapour, which includes a source term for vaporization and condensation processes (Ishii, 1975 and Saito et al, 2003), (iii) the models that focus on bubble evolution, which are usually based on the Rayleigh-Plesset equation (Plesset, 1948) or the Gilmore equation (Gilmore, 1952)
Summary
A new model based on bubble-bubble interactions is proposed for cavitation. They can be divided into three groups, according to the closure equation of the problem: (i) the barotropic models use a postulated equation of state that links the density to the pressure (Delannoy and Kueny, 1990; Coutier-Delgosha et al, 2003; and Koop and Hoeijmakers, 2006), (ii) the models based on a transport equation for the volume fraction of vapour, which includes a source term for vaporization and condensation processes (Ishii, 1975 and Saito et al, 2003), (iii) the models that focus on bubble evolution, which are usually based on the Rayleigh-Plesset equation (Plesset, 1948) or the Gilmore equation (Gilmore, 1952) Since they are based on the equations that govern the evolution of the cavitation nuclei, this third group of models may be the most appropriate to predict the phenomena involved in cavitation inception. Du et al (2016) have developed a cavitation model that includes phenomena of bubble breakup inside a cloud of bubbles, which provided simulations in agreement with experiments for configurations of developed cloud cavitation
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