Modeling the thermal behavior of an acoustically driven gas bubble.

Abstract

Numerical simulation of an acoustically driven gas bubble is usually achieved by solving a Rayleigh-Plesset-type equation, in which the time-dependent pressure of the gas inside the bubble needs to be appropriately modeled. This is done in most existing methods by assuming a polytropic relation between the gas pressure and the bubble volume, which sometimes oversimplifies the thermal interaction between the bubble and the ambient liquid. In this paper, a model is developed aiming to perform an accurate and efficient calculation of the pressure variation in the bubble. The approach is different from that in the recent paper by the author and his collaborator which used a combination of an integral and a collocation method to solve the energy equation in the gas [Zhou and Prosperetti (2020). J. Fluid Mech. 901, R3]. The starting point of the proposed method in this paper is the gas continuity equation which is manipulated to lead to three ordinary differential equations. In this way, the thermal behavior of an oscillating gas bubble is captured at a modest coding and computational cost.