The volumetric growth rate of individual grains as a function of their number of sides, as well as the average normalized volumetric growth rate for a given topological class are studied based on large-scale phase-field simulations of normal grain growth. For all cases, where different initial grain size distributions are considered, the same averaged normalized volumetric growth rate for a given topological class was obtained with the averaged normalized volumetric growth rate approximately zero for grains with Fo≈15$Fo\approx 15$ sides. The normalized average grain size as a function of topological class becomes constant within the transient regime and the relation in the transient and steady-state regime is similar and independent of initial grain structure. The relation does however not match Mullins' analytical model [W. Mullins, Acta Metall. 37 (1989) 2979-2984]. The effect of the average number of sides of the neighbouring grains on the average volumetric growth rate for a given topological class is analysed, as well. Moreover, tracking of the evolution of four grains suggests that the normalized volumetric growth rate of a grain is strongly linked with the number of sides of the grain at the given time.

基于正常晶粒生长的大规模相场模拟，研究了单个晶粒的体积增长率（随边数的变化）以及给定拓扑类别的平均归一化体积增长率。在所有情况下，考虑到不同的初始晶粒尺寸分布，对于给定的拓扑类别，均获得了相同的平均归一化体积增长率，其中对于Fo≈15的晶粒，其平均归一化体积增长率约为零。$FØ\approx 15$双方。归一化平均晶粒尺寸作为拓扑类别的函数在瞬态范围内变得恒定，并且在瞬态和稳态范围内的关系是相似的，并且与初始晶粒结构无关。但是，该关系与Mullins的分析模型不符。穆林斯，金属学报。37（1989）2979-2984]。还分析了给定拓扑类别的相邻晶粒的平均边数对平均体积增长率的影响。此外，跟踪四个晶粒的演化表明，在给定时间，晶粒的归一化体积生长速率与晶粒的边数密切相关。