An integral approach for simulation of vapour film dynamics around a spherical surface

The dynamics of a thermally driven vapour film around a solid sphere has been investigated here with both the sphere and the annular film surrounded by a large water pool. Integral models based on constant and variable vapour-phase densities have been developed here for studying a spherico-symmetric phase change problem for two immiscible phases, vapour and liquid around a hot sphere. Governing equations for both liquid and vapour phases are converted into a set of non-linear ODEs. Effects of distinct density on interface condition and density variation of vapour phase are taken into account both in energy equation of vapour phase and also in interfacial mass and energy balance. The present models have been validated with available analytical, incompressible Volume of Fluid (VOF) and experimental results of growth and collapse of either bubble or vapour film. A simple model, based on scale analysis, was evolved that successfully captured the non-monotonic growth of the film, as observed by the more detailed models under certain degree of liquid subcooling. In addition, the case of very small thermal boundary layer in the liquid side has been successfully studied for which the VOF model required very fine grid. It has been observed that the effect of density variation in the integral model results in marginally higher film growth at higher temperature. However, the effect of radiation on the film growth was found to be quite substantial. The integral model not only incorporates the effects of vapour-phase temperature variation and radiation exchange of heat but also is computationally several-fold efficient with respect to the VOF model.