Hierachical Multiscale Modeling of Positive Corona Discharges

TL;DR

The paper develops a hierarchical multiscale approach to model positive corona discharges by replacing the ionization region with emitter-surface boundary data for macro-scale drift-region simulations. It obtains this boundary information from detailed 1D full-scale cylindrical simulations that resolve the ionization layer, including photo-ionization, and fits an exponential injection law $n_p(E)=n_{ref}\expig[(E-ar{E}_{on})/E_{ref}ig]$ to describe ion emission as a function of the local field $E$ and emitter radius $R_e$. Validation against experiments shows strong agreement when photo-ionization is included, and the framework yields accurate current and ion-density predictions in both axisymmetric and 2D wire-cylinder configurations; without photo-ionization, the onset and current are less accurate. The work provides a practical pathway to efficient three-dimensional corona simulations by coupling macro-scale drift-diffusion with physics-informed boundary conditions derived from detailed full-scale modeling, with potential extensions to fully coupled fluid-structure interactions in propulsion and atmospheric applications. $E_{on}$, $S_{ph}$, and related quantities are used to connect scales, enabling accurate, scalable predictions of corona behavior across geometries.

Abstract

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.

Figures (26)

• Figure 1: Wire-in-Cylinder configuration of the electrodes. Emitter electrode is magnified for sake of clarity
• Figure 2: Sketch of the computational mesh.
• Figure 3: Current-voltage curves obtained from experimental results (Zheng et al. 2015) Zheng, numerical two-scale model (Monrolin et al. 2021) MonPlour, analytical model (Monrolin et al. 2018) Monrolin and 1-D simulation with Parent model with and without photo-ionization. Emitter radius $700\,\mu\text{m}$, gap $10.35\, \text{cm}$.
• Figure 4: Current-voltage curve obtained from full-scale simulations. Emitter radius $50\,\mu\text{m}$, gap $2\, \text{cm}$.
• Figure 5: Cumulative integral of the reaction rates, applied voltage $V_e=53\,\text{kV}$.