Development of One dimensional model for vapour-air Bubble Collapse

Abstract

The objective of the present work is to develop a one dimensional numerical model for predicting the rate of variation of bubble radius during the collapse of a spherical bubble containing some air. The bubble is assumed to contain homogeneous mixture of saturated vapour and air. Along with the mass balance and equation of state for vapour and air, the model integrates the discretized mass momentum and energy equation applicable for the surrounding liquid. The energy equation is cast in the Lagrangian form and is solved using finite volume methodology for an incompressible liquid. The model accounts for thermal effects by considering the apparent increase in liquid velocity due to condensate pile-up. This needs additional terms for mass flux due to phase change in the Rayleigh-Plesset equation along with the consideration of noncondensable gas content. The numerical results for the collapsing radius is compared with those obtained in experiments. The results show that the additional liquid growth velocity, V, plays an important role. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.