A simplified formulation of wire-plate corona discharge in air: application to the ion wind simulation

The spatial distribution of charged particles (electrons, negative ions and positive ions) and electric field have been evaluated using a semi-analytical approach of the positive and negative corona discharge for a wire-to-plate electrode system. Thus, approximate formulas useful for the characterization and control of corona discharge devices are provided, which helps to significantly reduce computational costs. Based on the obtained results, the electro-hydrodynamic (EHD) force generated by the corona discharge has been determined, and it has been used in the Navier-Stokes equations to compute the spatial distribution of the gas velocity. As a result, the influence of the corona plasma region in the flow pattern, particularly in the vicinity of the corona electrode, has been brought to light, which helps to understand the different flow velocities observed in positive and negative coronas. Moreover, the influence of voltage, wire radius, and inter-electrode separation on the electric wind velocity has been investigated

Multi-scale two-domain numerical modeling of stationary positive DC corona discharge/drift-region coupling

Corona discharge modeling mostly relies on two, mostly distinct, approaches: high-fidelity, numerically challenging, unsteady simulations having high-computational cost or low-fidelity simulations based on empirical assumptions such as constant electric field at the emitter electrode. For the purpose of steady discharge current predictions, high-fidelity models are very costly to use whilst empirical models have limited range of validity owing the subtle use of tuned parameters. We propose an intermediate approach: an asymptotic multi-scale/two-domain numerical modeling based upon generalizing previous asymptotic axi-symmetrical analysis [1,2]. We show how the initial elliptic (electric potential), hyperbolic (charge transport), non-local (photo-ionization) problem can be formulated into two local problems coupled by matching conditions. The approach relies on a multipole expansion of the radiative photo-ionization source term (in two dimensions for cylindrical emitters). The analytical asymptotic matching conditions derived in [2]result in flux continuity conditions at the boundary of the two domains. These coupling conditions are enforced by Lagrange multipliers, within a variational formulation, leading to a hierarchy of non-linear coupled problems. The proposed approach is both monolithic and two-domains: two asymptotic regions, an inner-one associated with corona discharge, and an outer-one, the ion drift region. Numerical convergence and validations of the finite element implementation is provided. A comparison with various experimental results convincingly demonstrate the applicability of the method, which avoids tuning parameters dedicated to each specific configuration, but, on the contrary, exclusively relies on known and measurable physical quantities (e.g.,ion mobilities, photo-ionization coefficient, ionization electric field, Townsend discharge coefficient, etc...)

Modélisation mathématique et numérique de décharges couronnes pour le contrôle d'écoulement

L'interaction entre une décharge couronne et un écoulement aérodynamique est un problème très difficile à simuler numériquement car fortement non-linéaire et multi-échelles, à la fois en temps et en espace. La présence d'une singularité de champ électrique induit en particulier une convergence en maillage lente et impose des contraintes sur le pas de temps localement très restrictives qui rendent les temps de calcul souvent prohibitifs. Cette thèse propose une méthode permettant une réduction significative du temps nécessaire à la simulation de ces décharges. Grâce à une analyse asymptotique dans un petit voisinage autour des électrodes, l'intégration numérique des équations plasma est remplacée par la résolution d'un problème approché, où seuls les principaux phénomènes de la dynamique de la décharge sont pris en compte. Dans cette zone, nous supposons en particulier que la décharge évolue principalement selon les lignes du champ électrostatique et qu'elle peut ainsi être décrite de manière monodimensionnelle. Dans le reste du domaine, la décharge est décrite à l'aide du modèle usuel associé à des conditions aux limites fictives provenant du modèle approché. Deux modèles sont présentés suivant ce principe. Le premier admet, sous certaines hypothèses, une solution quasi-analytique tandis que l'autre, plus précis, nécessite une résolution numérique. Une étude numérique poussée est ensuite effectuée sur des dispositifs aux dimensions réalistes. Celle-ci permet de valider l'utilisation de ces modèles et met en évidence, pour chacun des modèles, une diminution du temps de calcul d'un ordre de grandeur tout en conservant une précision similaire au modèle de référence.The interaction between a corona discharge and an airflow is a highly non-linear and multi-scale problem, in both time and space, and thus is very challenging to simulate numerically. In particular, the presence of a singular electric field leads to a slow mesh convergence and locally imposes very restrictive time step constraints that often lead to impracticable computational times. This thesis proposes a method that significantly reduces the time required to simulate such discharges. Using an asymptotic analysis in the vicinity of the electrodes, the numerical integration of the plasma equations is replaced by solving an approximate problem, where only the main phenomena of the dynamics of the discharge are taken into account. In this area, we assume in particular that the discharge development mainly follows the lines of the electrostatic field and can thus be described using a one-dimensional model. In the rest of the domain, the discharge is described using the reference model coupled with fictitious boundary conditions defined by the approximate model. Following this principle, two models are presented. The first one admits, under certain assumptions, a quasi-analytical solution while the other, more accurate, requires to be solved numerically. An extensive numerical study is then performed on experimental setups. The results validate the use of these models and show a decrease of the computation time by an order of magnitude while keeping an accuracy similar to the reference model