Fast and Accurate Numerical Modeling of Non-stationary Corona Discharges Based on Implicit Time Integration on Non-uniform Grid
Open Access
- Author:
- Tucker, Joseph Patrick
- Area of Honors:
- Electrical Engineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Victor P Pasko, Thesis Supervisor
Dr. Timothy Joseph Kane, Thesis Honors Advisor - Keywords:
- lightning
corona
thundercloud - Abstract:
- This Honors Thesis concerns the development of computationally efficient numerical models of non-stationary glow corona and streamer corona discharges in spherical geometry that approximate tall ground structures under thunderstorm conditions. Glow corona can occur when ambient electric field reaches modest values on the order of 0.2 kV/cm and when the electric field near sharp points of ground structure rises above a geometry dependent critical field required for ionization of air. Air is continuously ionized in a small region close to the surface of the structure and ions diffuse out into the surrounding air forming a corona. A downward leader approaching from a thundercloud causes a further increase in the electric field at the ground level. If the electric field rises to the point where it can support formation of streamers in air surrounding the tall structure, a streamer corona flash, or series of streamer corona flashes can be formed significantly affecting the space charge configuration formed by the preceding glow corona. The streamer corona can heat the surrounding air enough to form a self-propagating thermalized leader that is launched upward from the tall structure. This leader travels upward to- wards the thundercloud and connects with the downward approaching leader thus causing a lightning flash. Accurate time-dependent modeling of charge configura- tion created by the glow and streamer corona discharges around tall structure is an important component for understanding of the sequence of events leading to lightning attachment to the tall structure and represents the focus of this Honors Thesis. In comparison with previous work by Kowalski [2008] the model developed in this Honors Thesis uses an implicit numerical scheme for time integration and employs effective non-uniform grid system allowing very accurate description of non-stationary coronas emitted by sharp points with sub-millimeter dimensions and expanding hundreds of meters in surrounding air. Results are presented for different time dynamics of the applied electric field closely resembling scenarios under thunderstorm conditions, including, in particular, extended periods of time (tens of seconds) when only glow corona is produced, followed by a fast rise in the field (tens of microseconds) describing approach of the downward leader. This thesis also presents comparisons of the numerical model results on time dependent corona radius and current with an analytical corona theory summarized recently by Bazelyan et al. [2008].