On the calculation of heat transfer in a pulsating bubble

Abstract

This paper investigates the thermodynamic processes inside an isolated pulsating bubble which contains either ideal gas or saturated vapor. The study includes the effect of heat transfer across the bubble's free surface. For a bubble containing ideal gas, the equations developed by Prosperetti are adopted in the computer model. For the case of a bubble containing water vapor, an energy equation is used to model the processes of vaporization and condensation of vapor in the bubble. The transient heat flow in the liquid domain is modelled by a dual reciprocity boundary element technique. The energy equation is expressed in the form of an integral equation, which consists of a volume integration of the domain and an area integration over its boundary. The kernels of the domain integrals are approximated by interpolation functions, thereby reducing these integrals into boundary integrals. The results compare the rebound of an ideal gas bubble and a pure water vapor bubble. Some aspects of the modes of heat transfer across the bubble-liquid interface and the consequence of irreversibility are presented.