Reduced modeling of bubble clusters dynamics based on temporal scale separation

Simulation of cloud cavitation requires modeling the complex thermo-fluid dynamics of dispersed gas bubbles. Even the use of spherical bubble dynamics based on the Rayleigh-Plesset (RP) equation comes with a high cost due to the requirement of formulating inter-bubble interaction and resolving the violent collapse. In this study, we explore reduced modeling of bubble cluster dynamics based on multi-bubble RP-Keller-Miksis (RP-KM) equation. Our model is built on the approximate formulation of the R-P equation presented in Maeda and Fuster [J. Fluid. Mech., pp. 985, p.A23., 2024] that uses radius and velocity potential at the bubble surface as fast state variables and treats the temporal mean of the radius as a slow variable. This model performs well in the linear response regime but exhibits significant errors in the nonlinear regime under strong pressure excitation due to the underestimation of energy dissipation during bubble collapse. To overcome this, we perform systematic analysis of the error production and introduce a correction factor which controls effective damping during the collapse to compensate for the error. This corrected model is compared with the original RP-KM model through simulations of nonlinear regimes of bubble cluster dynamics with various nuclei parameters under various amplitudes of harmonic pressure excitation at O(1) MPa. Results show favorable agreement between the two models while maintaining several factors of cost reduction.