On the use of CALPHAD-based enthalpy-temperature relations in suboxidized corium plane front solidification modelling

Abstract

The knowledge of in-vessel corium behaviour and the associated risk of vessel failure are matters of prime interest within the framework of Severe Accident studies in a Light Water Reactor. As corium behaviour is dependent on associated thermochemical and thermohydraulic phenomena, its modelling within integral codes requires coupling between lumped parameter thermal models and thermochemical models.Such integral thermal models consist of mass and energy conservation equations that require inputs related to thermochemical properties of the materials, which are closely related to the state variables. In particular, the closure of energy conservation equations requires enthalpy-temperature relations. In the framework of multicomponent systems, the dependence of such relations to chemical composition is of importance and should be treated adequately to obtain a more accurate description of the phases depicted by the model. An approach to do so is to keep a general formulation of energy conservation equations in terms of specific enthalpies instead of substituting simplified enthalpy-temperature relations on a case-by-case basis in order to obtain models with an explicit temperature formulation. The enthalpy-temperature relation is then considered as an “Equation-of-State” (EOS) that can be written as: H:T,(wj)j∈S→h along with its reciprocal relation T:h,(wj)j∈S→T where (wj)j∈S is the composition of the phase in terms of species mass fraction, h the mass enthalpy and T the temperature.The present study demonstrates the feasibility of using CALPHAD-based enthalpy-temperature relations in the modelling of plane front solidification of suboxidized in-vessel corium. Along with theoretical considerations on the equations formulation, this paper discusses the use of associate models with species as its constituents for obtaining U-O-Zr thermodynamic description, owing to the sub-stoichiometric nature of (U,Zr)O2-x phase. As a result of incorporating such associate models, there is a need for modification of species conservation equations in order to evaluate interface quantities. The numerical results based on a model developed in the PROpagation of CORium (PROCOR) platform interfaced with the Open-Calphad thermodynamic software show the linearity of these EOS for solid and liquid phases with changing temperature and composition. The ‘almost’linear trends in the EOS confirm their usefulness in predicting system behaviour at macroscopic scales.