A TWO-PHASE MATHEMATICAL MODEL TO DESCRIBE DISSOLUTION OF A (U, Zr, O) SOLID CRUST BY LIQUID STEEL

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In case of the In-Vessel Retention (IVR) strategy, it is expected that the corium pool will be surrounded by an oxide crust, which will be in contact with molten steel from top of the pool as well as from sides of the vessel. It has been observed in CORDEB experiments that this crust becomes permeable, which has an impact on the thickness of molten steel layer, lying on top of it. With respect to the IVR strategy, a thin molten steel layer on top of the crust may lead to an excessive heat flux to the Reactor Pressure Vessel (RPV), resulting in a possible rupture or melt-through. Such phenomenon is commonly known as focusing effect. This paper deals with the study of dissolution of such crust in order to estimate the time for molten steel to flow through the crust. From a thermochemical point of view, corium is a mixture of UO2, ZrO2 and Zr. The chemical interaction between these species and Fe plays an important role in the stability (or not) of the crust. It is a quaternary interaction among U, Zr, Fe and O atoms. However, a thermochemical study of this system shows that it can be reduced to a pseudo-binary in each phase: (U, Zr) + O in the oxide phase and (U, Zr) + Fe in the metal phase. Consequently, in this paper, the complex quaternary dissolution is treated in a simplified way as the dissolution of a binary two-phase porous region by a liquid. An up-scaled model has been derived by volume averaging transport equations — Mass, Momentum and Species transport — over a Representative Elementary Volume (REV). The final system of Partial Differential Equations (PDEs) has been closed by deriving some empirical relations for the effective diffusivity in the phases and for the mass transfer coefficient between the phases. The model has been solved numerically over a 2D domain to study the progress of dissolution in the two-phase region. The numerical results are compared with CORDEB experiment results. The conclusions indicate that the effective diffusivity of species through the crust must be high, in order to reproduce the experimental observations. It is also shown that the behavior of crust depends on the boundary condition below it: if the oxide crust lies on the oxide pool, it should be stable, whereas if it lies on a metal layer it should finally be dissolved.

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