Governing equations for heat and mass transfer in heat-generating porous beds—II. Particulate melting and substrate penetration by dissolution

Abstract

Upon dryout of the bed, the dominant modes of heat transfer are conduction and radiation. Radiation is modeled through the Rosseland approximation. The melting of stainless-steel particulate imbedded in the fuel is modeled by assuming the bed to be a continuum with conduction and radiation as the dominant modes of heat transfer. The molten steel, after it drains to the bottom of the bed, is assumed to disappear into cracks and mortar joints of the MgO bricks. The melting of fuel in the interior of the bed is modeled identically to the steel particulate, except for the bed settling which is more pronounced in the case of fuel melting and is assumed to be instantaneous owing to the significant weight of overlying bed and sodium pool. The molten layer of fuel, as it collects at the bottom of the bed, causes the heatup of the MgO lining to the eutectic temperature (2280°C), and the MgO lining begins to dissolve. The density gradient caused by the dissolution of MgO leads to natural convection and mixing in the molten layer. The submerged fuel particulate also begins to dissolve in the molten solution and ultimately leads to the conversion of debris to a molten pool of fuel and MgO. The process of penetration of the MgO lining continues until the mixing process lowers the concentration of fuel in the volume of the pool to the level where the internal heat rate per unit volume is not enough to keep the body of the pool molten and leads to freezing in the cooler part of the pool. As the molten pool reaches a frozen or a quiescent state, the MgO brick lining thickness provided is deemed ‘safe’ for a given bed loading and the external rate of cooling.