Development of a robust, accurate and efficient coupling between PLEIADES/ALCYONE 2.1 fuel performance code and the OpenCalphad thermo-chemical solver

In this paper, a robust, accurate and efficient coupling between the PLEIADES/ALCYONE 2.1 fuel performance code and the OpenCalphad thermo-chemical solver is presented. A challenging 3.5D simulation of a power ramp, consisting of the 3D simulations of all the fuel pellets within a complete rodlet, serves as a base case to illustrate the difficulty inherent to extensive thermochemical equilibrium calculations (more than 1.5 million in this example) within fuel performance simulations, related both to the wide temperature and pressure range encountered in irradiated nuclear fuels. In the first part of this paper, a detailed analysis of the main quantities of interest (i.e. temperature, hydrostatic pressure, fission products concentration) is provided to illustrate the couplings at hand during a power ramp and, above all, to demonstrate the good agreement of the results with those already published in the literature and with available measurements of xenon, caesium and iodine releases. In the core of this paper, several numerical strategies are proposed to reduce the overall time spent in the thermochemical solver by defining at each node and for each time step a good initial estimate of the set of stable phases that are likely to form. The first one, referred to as the spatial strategy, relies on an intelligent reorganization of the mesh nodes as a function of temperature or hydrostatic pressure with an appropriate initialization of the thermochemical equilibrium calculation at a node by the phase composition calculated at the node with the closest thermo-mechanical conditions. The second strategy, referred to as the hybrid strategy, combines the spatial strategy during the power transient (where large power variations take place at each time step) with an initialization of the nodal equilibria from the solution obtained at the previous time step in case of small power variations. The 3.5D simulation has been run several times in order to assess and compare the spatial and hybrid strategies. The simulations show that the spatial strategy is the most efficient. It leads to an overall increase of the calculation time related to the incorporation of thermochemistry in the 3.5D fuel performance simulation of less than 2.25%, showing the feasibility of large thermal-chemical-mechanical simulations within the PLEIADES/ALCYONE 2.1 fuel performance code. Finally, as a first step towards more complicated simulations (i.e. including a greater number of phases and/or performed with a finer spatial discretization), a primitive parallelization algorithm based on a multiprocess approach is proposed. Combined with the most efficient spatial strategy, it leads to a substantial reduction of the extra (real) calculation time related to thermochemistry which become less than 0.65% of the total computation time when the thermochemical equilibrium calculations are distributed over 4 cores. (authors)