Optimization of an augmented Prosperetti-Lezzi bubble model

Abstract

Three enhancements are introduced for predicting the violent collapse and rebound of a spherical bubble with the matched-asymptotic-expansion model of Prosperetti and Lezzi [(1986). J. Fluid Mech. 168, 457-478]. The first introduces spatial variation of the pressure field inside the bubble. It derives from the perturbation analysis of the interior Euler equations begun by Geers et al. [(2012). J. Appl. Phys. 112, 054910]. The second enhancement augments the Prosperetti and Lezzi equation with a term that accounts for the kinetic energy of the bubble gas, while the third provides an optimum value for the free variable appearing in that equation. The optimum value emerges from a comparison of peak pressures predicted by the augmented equation with corresponding results generated by finite-difference simulations based on transformed Euler equations for both the bubble gas and the surrounding liquid [Geers et al. (2012). J. Appl. Phys. 112, 054910]. The three enhancements considerably extend the range of applicability of a single-degree-of-freedom bubble model.