A three-dimensional model of streamer discharges in unsteady airflow

Abstract

A 3D fluid model has been developed to simulate streamer discharges in unsteady airflow. The model couples the drift-diffusion equation for charged particles, the Navier-Stokes equations for air, the Poisson's equation for the electric field, and the Helmholtz equation for photoionization. It allows us to study electrical discharges at different timescales defined by light and heavy particles and to investigate the effects of unsteady airflow. The model treats the time integration in an implicit manner to allow longer time steps, which makes the simulation of long-duration discharges feasible. Moreover, the model uses an unstructured mesh allowing the calculation around solid bodies with complex geometries, and uses adaptive mesh refinement to lower the computation time. The validity and accuracy of the model has been verified by comparing its results with published results, which compares simulations in steady air from six different streamer codes. Our results are consistent and among the most accurate in terms of charge conservation. In order to investigate the influence of wind on streamer discharges, we present results from simulation of a long-duration discharge, in which two successive positive streamers are initiated from a positive polarity electrode in presence of a transverse airflow. This simulation shows that the impact of airflow on positive streamers is driven by the ions, and therefore the airflow effects are seen in ions timescale. Interestingly, we observe that the positive streamer channel, while tilting in the direction of the wind, remains attached to the surface of the electrode. The subsequent positive streamer emerges from the charges remaining from the initial streamer, which have been moved over the electrode surface toward the trailing edge. This mechanism shows and explains the clear tilting of the successive positive streamers in the direction of the wind.

Underlying mechanism of the stagnation of positive streamers

“…At this point, the field sharply decreases and the streamer vanishes. This behaviour was also found in our previous work, where we smoothed the ionization source based on a length scale depending on the local electric field [6]. We also note that as the streamer velocity reaches zero the streamer diameter reaches its minimum diameter of 0.12 mm.…”

“…The largest variable time step size is 5 ps. The implicit-ELP time integration scheme is chosen to remove the time step constraints from the Courant-Friedrich-Levy (CFL) stability condition and from the dielectric relaxation time [6,33]. The upwind spatial discretization scheme has been used.…”

DC-driven positive streamer coronas in airflow

“…The study of wind effects reveals novel observations compared to prior works [6,1]. The work by Vogel et al [6] and Niknezhad et al [1] reports on streamers tilting in the direction of wind.…”

“…In addition, flow patterns, such as recirculation bubbles or turbulent eddies, can temporarily trap or move ions, modifying the electric fields. The recent numerical results by Niknezhad et al [1] reveal that the long-lived (10 −5 s) ionization trail of a single positive streamer exposed to wind tilts in the direction of the wind, while remaining attached to the anode. The simulation also found that a successive streamer will follow the pre-ionized path of the previous streamer, adopting a curved shape in the direction of the wind.…”

“…Recent numerical studies have captured the effects of airflow on positive [1] and negative [2] streamer discharges, when exposed to lateral wind. Streamers are filamentary ionized structures that propagate at speeds of 10 5 to 10 6 m/s for 10 −8 to 10 −7 s in atmospheric pressure air [3,4,5], leaving behind an ionized channel.…”