Phase-change mechanism for evaporation in porous media using volume of fluid: Implicit formulation of interfacial temperature

Abstract

In this study, a widely-utilized mechanism which relates the rate of phase change in two-phase flows to an interfacial superheat is described and modified to improve its physical consistency and overall performance when compared to the porous two-phase Stefan problem. Maintaining interface temperature at saturation temperature, the rate of phase change is taken to be proportional to the degree of superheating at the interface. The present work demonstrates how the superheat error can be made to meet the same convergence requirements already established for the temperature solution at each time step by comparing the interfacial energy balance to the present methods superheat relation at the fluid-fluid interface. The results are in good agreement with the presented analytical solution for the porous media Stefan problem using propane. The Volume of Fluid (VOF) method, incompressible Navier-Stokes and temperature equations are segregated and modified to incorporate the effects of porous media and the source terms for phase change. For low porosities, a limitation of the rate of phase change is observed due to a restriction in the availability of interstitial pore space occupied by the phase change fluid. At the other extreme, when solid content diminishes, the system is reduced to the classical Stefan problem in free flow. Between these two ranges, an optimum porosity exists where the rate of phase change is maximum.