The temperature field and spatial distribution of metal vapor (i.e., flow field) are critical for the purity and direct yield of metals. However, it is impossible to accurately determine the temperature field and distribution of the metal vapor in a vacuum furnace. This study developed a surface-to-surface thermal radiation and volume of fluid multiphase flow coupling model. The temperature distribution and mass distribution of indium vapor in the vertical vacuum furnace at different temperatures from 1423 to 1573 K under the condition of 1 Pa were obtained. The reliability of the model was verified by experimental data obtained under the same conditions as the simulation. The temperature difference between the inside and outside of the condensing plate was 30–45 K in the temperature interval of 1423–1573 K. The temperature difference between the inside wall and the center of the condensing plate was 10 K. The simulation results of indium vapor mass distribution match with the experimental values; the overall temperature error is 5%, and the volatility error is less than 15%. The model developed in this study can be used to predict the temperature field and metal vapor distribution in a vacuum furnace, which will significantly reduce experimental exploration and accurately guide the production practice of vacuum metallurgy. This will expand the application of vacuum metallurgy technology in metal purification, material preparation, waste recycling, and other industries. This can effectively reduce exploratory experiments in the process of vacuum distillation to prepare high-purity metals, reduce the consumption of resources and energy in the experiment and production process, and achieve clean production.

中文翻译：

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真空蒸发金属铟温度和质量分布的模拟与实验研究

金属蒸气的温度场和空间分布（即流场）对于金属的纯度和直接收率至关重要。然而，准确确定真空炉内金属蒸气的温度场和分布是不可能的。本研究开发了表面到表面热辐射和流体体积多相流耦合模型。获得了1 Pa条件下1423~1573 K不同温度下立式真空炉内铟蒸气的温度分布和质量分布。通过与仿真相同条件下获得的实验数据验证了模型的可靠性。在1423~1573 K温度区间，冷凝板内外温差为30~45 K，冷凝板内壁与中心温差为10 K。 铟的模拟结果蒸气质量分布与实验值相符；总体温度误差为5%，波动误差小于15%。本研究开发的模型可用于预测真空炉内温度场和金属蒸气分布，将显着减少实验探索，准确指导真空冶金生产实践。这将扩大真空冶金技术在金属提纯、材料制备、废物回收等行业的应用。这可以有效减少真空蒸馏制备高纯金属过程中的探索性实验，减少实验和生产过程中资源和能源的消耗，实现清洁生产。