Coupling of the mixture model with the Rayleigh-Plesset equation

In numerical experiments for engineering applications cavitation is commonly addressed through the mixture model, which considers a scalar, indicating the vapor fraction transported by the flow. The sink and source terms of the transport equation, which rule the dynamics of the cavity, can be expressed through different models. They rely on the use of coefficients which accelerate/decelerate the vaporization and condensation processes and which are usually calibrated through optimization methods. According to the Sauer-Schnerr (SS) model the vapor fraction is related to the bubble dynamics and a simplified version of the Rayleigh-Plesset (RP) equation is exploited to evaluate the bubble radius growth/decrease. We propose the coupling of the SS model with the complete RP equation. Retaining all the terms of the RP equation allows to observe the typical rebounds of bubbles and their influence on the vapor phase development. We test the proposed model by considering a benchmark case, for which experimental data are available. The results are also compared with those obtained with the standard formulation of SS model. We point out how the accurately reproduced high-frequency dynamics of the cavity may be important for the acoustic characterization of cavitating flows.