Multi-Physics and Multi-Scale Modeling and Simulation Methods for Nuclear Reactor Application

U₃Si₂ is a potential accident-tolerant fuel (ATF) due to its high thermal conductivity and uranium density relative to UO₂. The grain size and distribution play an essential role in the service performance of U₃Si₂. However, the grain evolution is quite complicated and remains unclear, which limits further application of U₃Si₂ in the ATF assembly. In the present work, a phase-field model is employed to investigate the nucleation and growth of grains in U₃Si_2. Our results show that the number of grains rises rapidly at the nucleation stage until they occupy the whole system. After that, the grain radius and area continue to grow, and the grain number decays. The grain area increases in time according to the linear law, while the mean grain radius increases with time in a power law form with the scaling growth exponent z = 0.42, which is quite close to the theoretically predicted value. Finally, we performed statistical analysis and found that the grain size evolution of U₃Si₂ obeys Rayleigh distribution. Our simulation not only elucidates the nucleation and evolution of grains in U₃Si₂ during the thermal treatment process unambiguously but also provides a fundamental study on the investigation of grain growth, subdivision, and even amorphization in the irradiated condition, which is very important for U₃Si₂ used as ATF in the light water reactor.

A parallel Jacobian-Free Newton Krylov discrete ordinates method (comePSn_JFNK) is proposed to solve the multi-dimensional multi-group pin-by-pin neutron transport models, which makes full use of the good efficiency and parallel performance of the JFNK framework and the high accuracy of the Sn method for the large-scale models. In this paper, the k-eigenvalue and the scalar fluxes (rather than the angular fluxes) are chosen as the global solution variables of the parallel JFNK method, and the corresponding residual functions are evaluated by the Koch–Baker–Alcouffe (KBA) algorithm with the spatial domain decomposition in the parallel Sn framework. Unlike the original Sn iterative strategy, only a “flattened” power iterative process which includes a single outer iteration without nested inner iterations is required for the JFNK strategy. Finally, the comePSn_JFNK code is developed in C++ language and, the numerical solutions of the 2-D/3-D KAIST-3A benchmark problems and the 2-D/3-D full-core MOX/UOX pin-by-pin models with different control rod distribution show that comePSn_JFNK method can obtain significant efficiency advantage compared with the original power iteration method (comePSn) for the parallel simulation of the large-scale complicated pin-by-pin models.