Hierarchical multiscale modeling of positive corona discharges

In the field of corona discharges, the complex chemical mechanisms inside the ionization region have prompted the development of simplified models to replicate the macroscopic effects of ion generation, thereby reducing the computational effort, especially in two and three dimensional simulations. We propose a methodology that allows to replace the ionization process with appropriate boundary conditions used by a corona model solving the drift region. We refer to this model as macro-scale, since it does not solve the ionization region. Our approach begins with one dimensional computations in cylindrical coordinates of the whole discharge, where we include a fairly detailed model of the plasma region near the emitter. We refer to this model as full-scale, since all the spatial scales, including the ionization region, are properly taken into account. From these results it is possible to establish boundary conditions for macroscopic simulations. The idea is that, given an emitter radius, the boundary conditions can be used for a variety of geometries that leverage on that emitter as active electrode. Our results agree with available experimental data for positive corona discharges in different configurations and with simplified analytical models from literature.