The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, fV, was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p. The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of fV vs. p did not change significantly. The percolation threshold pc was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

中文翻译：

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U-(Pu)-Zr 核燃料中裂变气泡生长和互连的相场模拟

使用相场模型模拟了 U-(Pu)-Zr 核燃料较热中心区域裂变气泡的生长和相互连接。Cahn-Hilliard 方程用于表示具有单一缺陷种类的两相微观结构。在生长和互连过程中确定了气泡相的体积分数和气泡-基质界面的表面积。表面积在生长的初始阶段迅速增加，然后随着气泡互连开始而减慢并最终减少，并且粗化作用降低了表面积。排放到模拟域边界的气泡分数 fV 被量化为微观结构互连性的量度，并绘制为孔隙率 p 的函数。缺陷种类扩散率是变化的；尽管扩散率的变化显着影响了微观结构，但 fV 与 p 的图没有显着变化。渗透阈值 pc 被计算为大约 0.26，这取决于假设的扩散率并使用基于实验观察的初始气泡数密度。这略小于重叠 3D 球体的连续渗透的渗透阈值。模拟结果用于参数化核燃料性能代码 BISON 中 U-(Pu)-Zr 的两种不同工程规模的膨胀模型。这略小于重叠 3D 球体的连续渗透的渗透阈值。模拟结果用于参数化核燃料性能代码 BISON 中 U-(Pu)-Zr 的两种不同工程规模的膨胀模型。这略小于重叠 3D 球体的连续渗透的渗透阈值。模拟结果用于参数化核燃料性能代码 BISON 中 U-(Pu)-Zr 的两种不同工程规模的膨胀模型。