Numerical investigation of the role of heat transfer in bubble dynamics

Abstract

Bubble dynamics is generally described by the well-known Rayleigh-Plesset (R-P) equation in which the bubble pressure (or equivalently the bubble density) is predefined by assuming a polytropic gas equation of state with common assumptions to include either isothermal or adiabatic bubble behaviour. The present study examines the applicability of this assumption by assuming that the bubble density obeys the ideal gas equation of state, while the heat exchange with the surrounding liquid is estimated as part of the numerical solution. The numerical model employed includes the solution of the Navier-Stokes equations along with the energy equation, while the liquidgas interface is tracked using the Volume of Fluid (VOF) methodology; phase-change mechanism is assumed to be insignificant compared to bubble heat transfer mechanism. To assess the effect of heat transfer and gas equation of state on bubble behaviour, simulations are also performed for the same initial conditions by using a polytropic equation of state for the bubble phase without solving the energy equation. The accuracy of computations is enhanced by using a dynamic local grid refinement technique which reduces the computational cost and allows for the accurate representation of the interface for the whole duration of the phenomenon in which the bubble size changes significantly. A parametric study performed for various initial bubble sizes and ambient conditions reveals the cases for which the bubble behaviour resembles that of an isothermal or the adiabatic one. Additional to the CFD simulations, a 0-D model is proposed to predict the bubble dynamics. This combines the solution of a modified R-P equation assuming ideal gas bubble content along with an equation for the bubble temperature based on the 1 st law of thermodynamics; a correction factor is used to represent accurately the heat transfer between the two phases. KeywordsBubble dynamics, heat transfer, CFD-VOF model, 0-D model. IntroductionThe need for the inclusion of thermal effects in bubble dynamics was first addressed in [1] among others; it was shown that the polytropic gas assumption may provide inaccurate predictions of the bubble behaviour when thermal processes are taken into consideration. Since then, the effect of heat and mass transfer on bubble dynamics were examined in a large number of studies, either by CFD numerical models that are capable of solving the complex equations that characterize the physical processes of the bubble motion, or by reduced order models which include various assumptions but are computationally more efficient. In the framework of the CFD studies, the effect of heat transfer by solving the equation of gas-vapour bubble including variation of liquid temperature and assuming liquid incompressibility was examined in [2]. The main assumption in this study, was that the temperature distribution inside the bubble to be uniform, which allowed the authors to integrate analytically the continuity and momentum equations inside the bubble. In [3], the motion ...