Phase-field modelling and simulations of phase separation in the two-phase nuclear glass na2o-sio2-moo3

Overview & Synopsis

A safe and convenient method for the containment of nuclear waste is its inclusion in nuclear glasses, which are specifically designed to provide the best chemical, thermal and radioactive isolation. The SIVIT (SImulation of VITrification) project of the CEA studies the behaviour of the glass during the vitrification process, where the glass and the waste are mixed and brought to a high temperature and then solidified. It is desirable to control a whole set of macroscopic properties (chemical, thermodynamic, mechanical...) in the produced material, and one of them in particular is the possible occurrence of phase separation. For example, during the vitrification of waste enriched in molybdenum, phase separation may occur following the nucleation and growth regime, with the molybdenum segregating to the daughter phase. The present work, as part of the SIVIT project, aims to model and simulate this phase separation at the scale of the interface separating the two liquid phases of the melted glass. To this end, the modelling must satisfy a number of constraints: tracking a fully-resolved interface; accounting for the chemical diffusion (which drives the growth dynamics) and the flow dynamics and the effects of each on the motion of the interfaces; and the respect of the equation of state of the glass. We will first examine the case of a model ternary glass, the Na2O-SiO2-MoO3 compound. Its phase diagram was established at the CEA of Saclay, and experimental observations with this glass are being carried out at the CEA of Marcoule. Simulations of the model must also have a high numerical efficiency to allow for comparisons in three dimensions at a satisfying scale with the previously mentioned observations. To fulfil these requirements, we formulate a model based on the phase field theory with a grand potential formulation coupled to the diffusion of the chemical components and to the incompressible Navier-Stokes equations. We discretise this model with the lattice Boltzmann method and implement it in a new high-performance simulation code, LBM_saclay, able to exploit the multi-GPU architectures of modern supercomputers. We then demonstrate the capability of the model to quantitatively reproduce the growth dynamics after nucleation and the influence of flow and sedimentation on these dynamics. This is done with an idealised equation of state. Finally, we detail at the end the method to couple the model to the thermodynamic data of the real nuclear glass.