An Integral Approach for Predicting Vapour Film Collapse and Growth Around a Hot Sphere in Subcooled Water

Abstract

The phase-change heat transfer has attracted researchers for its wide range of industrial applications like solidification in liquid containers, cooling of phase change material storage, combustion of spherical droplets and vapour explosion with associated film boiling and film collapse around molten drop in a coolant liquid. Major features of phase-change processes are heat transfer among multiple phases, mass transfer caused by latent heat of phase change and movement of phase interface. In present work a sphericosymmetric numerical model is developed to predict very rapid collapse of a vapour film around a hot melt immersed in a pool of subcooled water. The governing equations for the vapour film and the liquid were transformed into a number of non-linear ordinary differential equations by an integral approach assuming a quadratic temperature profile in both vapour and liquid domain while the melt was modelled as lumped mass. The energy balance across liquid vapour interface was incorporated by an equilibrium phase change model. The contribution of radiation from melt to the interface was considered assuming the vapour film to be non-participating. The non-linear ODE-s was solved by a fourth order Runge-Kutta method. The model was validated against some of the available solutions of liquid-vapour system. The present model shows excellent agreement in predicting growth of a solidification front in a saturated liquid (Stefan problem). The growth of a bubble in a superheated liquid was also validated with the available analytical solution. The results obtained from developed model for film collapse and growth around a hot melt in subcooled liquid were compared with a more accurate numerical model based on Volume of fluid method (VOF). It is found that the present model is able to capture successfully the rapid collapse of film due to condensation with computational time of one order less as compared to VOF based model. The film shows a very fast rebound (~ ms) due to faster condensation around liquid-vapour interface, following which a slower growth of vapour film is observed for different subcooling level.