通过将二维Bejan计算模型扩展到三维，研究Gr=103情况下排列数范围为3×3至15×15的水平单层球自然对流换热情况。研究发现：随着排列数增加，卷流作用的增强使得单层球上方区域负压增大，导致通过球体间隙从下方吸入的流体速度升高，进而强化球体和流体之间的换热；由于排列数对上游区域温度边界层影响更大，该区域Nu数受其影响更明显。此外，拟合得到中心球的Nu数和N之间的关联式。基于极限的数学思想，该关联式可以预测不受周围球数增加影响的中心球的Nu数为4.162 8，这比Gr数相同情况下的单球的Nu数下降30.2%。该研究既能优化加速器驱动次临界堆系统流态固体靶结构的设计，也能为其他包含大数量多球系统的工业应用提供一定的参考价值。
With the three dimensional computational model extended based on that by Bejan in two dimensional condition, natural convection heat transfer from the single-layer horizontal spheres under the aligned arrangement is numerically investigated at Gr=103 for array changing from 3×3 to 15×15. The study found that with the increase of the number of array N, the plume makes the absolute value of negative pressure above the single-layer spheres bigger, which leads to the acceleration of air sucked up through the gaps among the spheres, thereby enhancing heat transfer; the local Nu number in the upstream of the spheres is more affected by the arrangement number since it has a greater influence on the temperature boundary layer in this region. Furthermore, the correlation of the average Nusselt number Nu of the central sphere with the arrangement number N is obtained, which could be predicted by the idea of limit in mathematics that the central sphere of the single-layer spheres has a Nu number of 4.162 8 that is not affected by the increase of the number of surrounding spheres,which reduces by 30.2% than that of single sphere at same Gr number. It provides some value of reference not only for the optimal design of the granular flow target of the accelerator driven subcritical system in China, but also for other industrial applications including multi-spherical systems.
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