Last modified: 19-07-2017

#### Abstract

Bubble dynamics is generally described by the well-known Rayleigh-Plesset (R-P) equation in which the bubblepressure (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 liquid- gas 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 bubbletemperature based on the 1st law of thermodynamics; a correction factor is used to represent accurately the heattransfer between the two phases.

DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4691