A closed-form solution for the deposition of atmospheric particulate matter on electrical insulators

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.