Melting and refreezing of porous media

During severe nuclear reactor accidents similar to Three-Mile Island, the fuel rods can fragment and thus convert the reactor core into a large rubble bed composed primarily of UO₂ and ZrO₂ particles. In the present study a one-dimensional model is developed for the melting and refreezing of such a bed. The analysis includes mass conservation equations for the species of interest (UO₂ and ZrO₂); a momentum equation that represents a balance among drag, capillary and gravity forces; an energy equation that incorporates the effects of convection by the melt, radiation and conduction through the bed and internal heat generation; and a UO₂---ZrO₂ phase diagram. A few key results are that (1) capillary forces are only important in beds composed of particles smaller than a few millimeters in diameter and in such beds, melt relocates both upward and downward until it freezes, forming crusted regions above and below the melt zone; (2) as melt flows downward and freezes, a flow blockage forms near the bottom of the bed and the location of this blockage is determined by the bottom thermal boundary layer thickness; (3) the maximum thickness of the lower crust increases linearly with the height of the bed; and (4) deviations from initially uniform composition profiles occur because ZrO₂ is preferentially melted and these deviations decrease as the initial ZrO₂ concentration is increased.