Spatio-temporal analysis of electrostatic discharge during accumulation with dynamic iterative modeling

A strong electric field and intense electrostatic discharge (ESD) are intimately related to the ongoing accumulation of high charge-mass ratio (CMR) particles. The ESD type, frequency, and electrostatic energy resulting from particle accumulation are critical factors in tragedy; however, they cannot be monitored in real time online. Therefore, a dynamic iterative model is presented in this study to analyse the spatiotemporal evolution of ESDs. The discharge threshold is regarded as the constraint border, and the spatial charge density is used as the control variable to solve the electric field. It separates the particle heap into thousands of regions, setting each region a spatial charge density. The electric field strength and discharge threshold are compared to identify the ESD location. The entire accumulation is split into many stages to calculate the spatiotemporal electric field and electrostatic energy. The ESD type and frequency are ascertained once the ESD regions are obtained on the basis of the electric field strength. These findings provide reliable evidence that under conical silos and heaps, broad and linear discharges with greater frequency and electrostatic energy can cause significant damage. Consistent with other experimental data, the dynamic model effectively offers a step-by-step evolution to highlight the effect of time on ESDs, where the electric field strength varies around the discharge threshold.