Analysis of sheet cavitation with bubble/bubble interaction models

Abstract

A new cavitation model based on bubble/bubble interactions has been recently proposed by the authors Adama Maiga, Coutier-Delgosha, and Buisine [“A new Cavitation model based on bubble-bubble interactions,” Phys. Fluids 30, 123301 (2018)]. It includes all nonlinear interaction terms between two bubbles, and the only input is the local velocity divergence, while the classical Rayleigh-Plesset or Gilmore models only take into account the linear interaction terms and require the local pressure evolution. In this previous publication, the model has been validated against cases of single bubbles growths and collapses. In the present paper, the same model is applied to configurations of high-speed cavitating flow on a Venturi profile and a two-dimensional foil section, where experiments based on X-ray imaging have been recently conducted. Based on the flow velocity fields available in the two cases, the local velocity divergence is calculated, and a one-dimensional mean divergence evolution from the leading edge to the wake of the cavity is extracted and used as an input for the model validation. The evolutions of the biggest bubble and the volume of vapor are both found in good agreement with the experiments. A typical velocity divergence evolution is then defined, and our model is compared to the modified Rayleigh-Plesset equation that includes the interactions between multiple bubbles. It confirms that the radius evolution of the biggest bubble is systematically better estimated by the new model due to its capability to continuously take into account the interactions of big bubbles with smaller bubbles. Eventually, the model is used to investigate the scale effect, by applying 6 different time scales of cavitation development covering more than 5 orders of magnitude. It is shown that the bubble size does not vary proportionally to the scale, but according to a law that is empirically determined.