The present study provides a simplified closed-form solution for the deposition flux of atmospheric Particulate Matter on electrical insulators. Due to the lack of experimental data on deposition over this type of solid bodies, the mathematical model is closed by means of a 4D regression procedure on obstacle-scale numerical data. This dataset is obtained with the Lagrangian Stochastic Model SPRAY-WEB (Università del Piemonte Orientale et al., 2021). The code was already validated on Particulate Matter dispersion and deposition on solid obstacles (Amicarelli et al. in Environ Fluid Mech 21(2): 433–463, 2021) and is here applied to a XP-70 porcelain-disk electrical insulator. A published tutorial is associated with this numerical dataset (SPRAY-WEB, 2021). The verification metrics on the performance of the closed-form solution show that the errors lie below the guideline thresholds for air-quality numerical simulations (Chang and Hanna in Meteorol Atmos Phys 87:167–196, 2004) and are limited by a Maximum Gross Error of ca.24% for an external verification. Although they cannot be used to close any mathematical model or to represent any specific event, the long-term averaged deposition fluxes of Zhang et al. (IEEE Trans Dielectr Electr Insulat 21(4):1901–1909, 2014. 10.1109/TDEI.2014.004343) are associated with the same insulator used for this study. With respect to the full-scale experiment mentioned above, the present solution provides an overestimation of 13%. The closed-form solution can be used for instantaneous preliminary estimates or be integrated within air-quality numerical codes for fast assessments of contamination maps for electrical insulators. Such applications aim to quantify the insulator functional damage (i.e., flashovers, short-circuits). The closed-form solution can be also generalized any time new data are available.

本研究为大气颗粒物在电绝缘体上的沉积通量提供了一种简化的封闭式解决方案。由于缺乏此类固体上沉积的实验数据，数学模型通过障碍物尺度数值数据的 4D 回归程序来封闭。该数据集是使用拉格朗日随机模型 SPRAY-WEB（Università del Piemonte Orientale 等人，2021 年）获得的。该代码已在固体障碍物上的颗粒物分散和沉积方面得到验证（Amicarelli 等人，Environ Fluid Mech 21(2): 433–463, 2021），并在此处应用于 XP-70 瓷盘电绝缘体。已发布的教程与此数值数据集相关联（SPRAY-WEB，2021）。封闭式解决方案性能的验证指标表明，误差低于空气质量数值模拟的指导阈值（Chang 和 Hanna 在 Meteorol Atmos Phys 87:167–196, 2004），并且受到最大毛重的限制外部验证的误差约为 24%。虽然它们不能用于关闭任何数学模型或表示任何特定事件，但 Zhang 等人 的长期平均沉积通量。（IEEE Trans Dielectr Electr Insulat 21(4):1901–1909, 2014. 10.1109/TDEI.2014.004343）与本研究使用的相同绝缘体相关。对于上面提到的全尺寸实验，本解决方案提供了 13% 的高估。封闭式解决方案可用于瞬时初步估计或集成到空气质量数字代码中，以快速评估电绝缘体的污染图。此类应用旨在量化绝缘子功能损坏（即闪络、短路）。每当有新数据可用时，也可以推广封闭形式的解决方案。