Theoretical modelling of the development of the positive spark in long gaps

Abstract

The main purpose of this paper is to present a physical model of the positive discharge in long air gaps. A large number of previous experimental and theoretical studies led to the identification of the different successive phases of the spark development: formation and propagation of first corona streamers, inception of the conductive stem at the electrode tip, formation and development of second corona (or 'leader corona') from the stem, and, eventually, the propagation of the leader and leader corona system until the final jump preceding the arc onset. Details of the specific modelling of each phase is presented, using the classical equations for conservation of mass, momentum and energy for each particle species. These basic equations are simplified according to the dominant electrostatic, hydrodynamic or thermodynamic processes involved in each step of the spark development. The resulting models for simulation of the corona and leader phases are coupled with an analytical calculation of the electric field due to the electrodes, the leader channel and the space charge injected into the gap. The different phase simulation models are expressed with a homogeneous simplification level and then linked sequentially into a complete model, which performs the step-by-step simulation of all the successive discharges phases until the final jump. The model described here is self-consistent since the only input data are the electrode geometry and the applied potential wave-shape. A good agreement between computed and experimental results has been obtained in various test configurations; the model has been also used to simulate the discharge behaviour with perturbations of the applied potential wave and permits the analysis of the conditions for stable propagation of the positive leader. It is shown that some parameters of practical interest, as the 50% breakdown voltage or the time to breakdown can be derived from the proposed model.