Modelling of electric discharges in unsteady airflow

Although lightning had been studied extensively from the pioneering experiments of Benjamin Franklin and Jacques de Roma about two centuries ago, many questions related to the initiation, propagation, and termination of electric discharges in the atmosphere are still open. This work is motivated by the lightning protection of wind turbines that may be hit by lightnings on frequent basis. One of the main questions is the understanding of how a lightning is influenced by the wind.

In this thesis, we study the effects of airflow on electric discharges. We focus on the building blocks of lightning: the streamers and study specifically the influence of airflow on positive streamers and negative coronas. It allowed us to thoroughly investigate the stagnation of positive streamers and the negative coronas of type Trichel pulse. To conduct the studies, we have developed a three-dimensional model of streamer discharges in unsteady airflow which is particularly designed for the simulation of long-duration discharges. The model couples the electric discharge dynamics and the Navier-Stokes equations for air. The model is based on an unstructured grid to incorporate solid bodies with complex geometries allowing us to investigate the nonuniform electric fields produced by non-flat electrodes. Furthermore, the model uses implicit time integration scheme which removes the time step constraints imposed by the Courant-Friedrichs-Lewy (CFL) and the dielectric relaxation time.

The model uses adaptive mesh refinement to concentrate the mesh in regions with high electric field and high density gradients helping to further reduce the computation time. We have evaluated the accuracy and performance of our model by comparing its results to the ones from a streamer discharge simulation in steady air from six different codes. Our results agreed with other models and performed particularly well in conserving the charges even when taking long time steps.

To illustrate the effects of the airflow on the positive streamers, we report the results of a long-duration simulation of two consecutive streamer pulses while being exposed to a lateral wind. The 1st streamer initiated from a neutral plasma patch have an insignificant deflection in the wind direction demonstrating that the effects of low-speed airflow on positive streamers are negligible during its propagation. In the long time between the first and second streamer pulses, the wind moved the charges from the 1st streamer channel over the surface of the anode, which interestingly remained attached to the surface of the anode. The 2nd streamer was initiated from the charges left by the 1st streamer which were moved over the anode surface toward the downwind. The 2nd streamer showed a significant tilting in the wind direction indicating that the influence of airflow on positive streamers manifest itself on longer timescales than the streamer timescale.

We similarly investigated the effects of the unsteady airflow on negative corona discharges. The simulation involves the initiation and termination of two consecutive negative corona pulses in a transversal airflow similar to the positive streamer simulation. We observe that the influence of airflow on the negative coronas are not as noticeable as compared to what observed for positive streamers. The negative corona tilts only slightly in the direction of the wind. Interestingly, we observe the formation of a positive streamer above the cathode surface which propagates toward the cathode and marks the onset of the second Trichel negative corona current pulse (NCCP). Previous studies of the mechanism behind Trichel negative corona pulses had suggested the presence of such mechanism. We present the steps in the initiation, propagation and stagnation of this streamer and show its agreement with the current waveform.

Furthermore, we investigate the positive streamer stagnation as it exhibits a complicated behavior which resulted in streamer tip electric field instability. As the streamer propagated away from the electrode, the streamer narrowed down and the tip electric field increased which at some point became unbounded and the simulation terminated. We hypothesize that this instability is due to the local field and density approximation in the calculation of the ionization source term from the drift-diffusion model. In order to relax the local density approximation, we used an extended drift-diffusion model based on the gradients of electron density. The result form the non-local extended model shows a stable streamer propagation where streamer tip electric field remains bounded during the stagnation process. Moreover, we report on the ultimate stages of positive streamer stagnation which is associated with a sharp decrease in the streamer tip electric field