I-D simulation of a spark discharge in air

Abstract

The development and radial expansion of a spark is simulated using a finite element method. The caleulations start from a weakly conducting channel as left by the passage of a streamer. Plasma heating during break down is provided by an L-C combination resembling the equivalent circuit of the spark plug. Once the effective current provided by this circuit drops below a certain level, a current source with a linearly decreasing current with time was used to model the subsequent arc or glow phases. The simulations cover a time range from nanoseconds up to 10 μs, when the axial symmetry of the channel is broken by 2-D effects such as reverse gas flow along the electrodes. It is shown that equivalent plasma kernels can be produced by assuming initial conditions where the breakdown energy is deposited within a very small cylindrical volume of ambient mass density. This also causes the emission of a strong shock which is indispensable for the achievement of same shape of the kernel. Calculations for ambient pressure and temperature as well as for 5 bar/550 K were conducted. The influence of the breakdown energy, the radiation, and the current delivered by the current source on the fully evolved spark channel is discussed. It is suggested how to use the calculated thermodynamic properties of the plasma kernel as initial conditions for flame-kernel calculations using a chemical reaction scheme. The fluid-mechanical Euler equations, including thermal conductivity, radiation losses, and Joule heating, are implemented using a Taylor-Galerkin formalism. The electric field is calculated using a time-independent potential formulation. This is implemented in the frame of the finite element program Flux Expert (Flux Expert is a registered trademark of DT2i).