The Sodium-Cooled Fast Reactor (SFR) system, which features a fast-spectrum, sodium-cooled reactor and a closed fuel cycle for efficient management of actinides and conversion of fertile uranium, is rather prominent in the nuclear reactor design in Generation IV (Gen IV), and likely to be widespreadly used and well-constructed all over the world. However, molten sodium may be sprayed into the ambient or secondary side of steam generator, induced by the pressure drop, in case of an inevitable break in the primary system. This kind of leakage can result in sodium spray fire accident, as a result of the chemical activity of sodium, significantly damaging the equipment and working staffs nearby. Sodium spray fire, which occurs not only in the nuclear industry, but also in solar industry, is a complex process consisting of several specific phenomena, such as the spray dynamics (e.g. droplet particle size/velocity distribution, particle collision and agglomeration), droplets evaporation, sodium aerosol diffusion, thus being drawn many experts’ attention. Based on International Atomic Energy Agency (IAEA)’s effort on phenomena identification and ranking table (PIRT) for sodium spray fire, prediction of droplet size distribution and the mean diameter in particular, are supposed to be in the very first place at level 2, due to the lack of available experimental data for both of model development and validation, and code inadequacy, as well. In this paper, sodium droplet size distribution model is theoretically derived, regarding both of mass and momentum equations as constraints, based on the maximum entropy principle, which can quantitatively describe the effects of two main influencing factors, including initial injection velocity and thermophysical properties of molten sodium. This analytical model is implemented in three typical conditions, including two sodium droplets size distribution experiments and one water droplet experiment. Validations against both of the available test data and predictions by an empirical model, named of Nukiyama-Tanasawa correlation, are conducted with the relative error of median diameter ranging from 17.3% to 18.2%, which ensures the reliability and feasibility of the new model. Moreover, sensitivity analyses are carried out, in terms of typical test conditions of sodium spray fire, which demonstrates that the median diameter of droplets’ size decreases with both of the increase of initial injection velocity and sodium temperature, thus probable triggering positive effect on the propagation of the accident, due to rapid interaction of violent chemical reaction and sodium spray. Besides, the present work can provide a reliable analytical model for the development of safety analysis codes for SFRs.

钠冷快堆（SFR）系统具有快速光谱，钠冷反应堆和封闭式燃料循环系统，可有效控制act系元素和可转化铀，在第四代核反应堆设计中相当突出（第四代），并且可能会在世界范围内广泛使用和构造良好。但是，在一次系统不可避免的破裂的情况下，由于压力下降，熔融的钠可能会喷入蒸汽发生器的周围或二次侧。由于钠的化学活性，这种泄漏会导致钠喷雾着火事故，从而严重损坏附近的设备和工作人员。钠喷雾火不仅发生在核工业中，而且还发生在太阳能工业中，是一个复杂的过程，由几种特定现象组成，诸如喷雾动力学（例如，液滴粒径/速度分布，颗粒碰撞和团聚），液滴蒸发，钠气溶胶扩散等，因此引起了许多专家的关注。根据国际原子能机构（IAEA）在钠雾燃烧现象识别和分级表（PIRT）方面的努力，预计液滴尺寸分布（尤其是平均直径）的预测在2级处于首位，原因是缺乏用于模型开发和验证的可用实验数据，以及代码不足。本文基于最大熵原理，以质量和动量方程为约束，从理论上推导了钠滴尺寸分布模型，该模型可以定量地描述两个主要影响因素的影响，包括初始注射速度和熔融钠的热物理性质。该分析模型是在三种典型条件下实现的，包括两个钠滴大小分布实验和一个水滴实验。通过一个名为Nukiyama-Tanasawa相关性的经验模型对可用的测试数据和预测进行验证，其中值直径的相对误差范围为17.3％至18.2％，这确保了新模型的可靠性和可行性。此外，针对钠喷雾火焰的典型测试条件进行了灵敏度分析，结果表明，液滴的中值直径随初始注入速度和钠温度的增加而减小，因此，由于剧烈的化学反应和钠喷雾的快速相互作用，可能对事故的传播产生积极影响。此外，目前的工作可以为开发SFR的安全分析代码提供可靠的分析模型。