Mathematical model

Kinetic estimates

This section reports a study of the chemical kinetics of SF6. During arc decay, strong blowing occurs and the column of plasma can be locally cut by a layer of cold gas with a very low electrical conductivity preventing the electric current from circulating. The input of this cold gas in the hot regions of the plasma tends to cause the disappearance of electrons. In this study, we investigate the molecular species (SFX (X=2 to 6), S2, SF and F2), which, under the influence of convection, can reach the hot zones. We will look at the species that favour electron disappearance and the dominant reactions involved.

The general chemical reaction of dissociation or recombination between atoms and molecules is given by relation (3), were Kd represents the direct rate and Ki the reverse rate.
At equilibrium, the rate of direct reactions is equal to the rate of reverse reactions per unit time and volume (4). The relaxation time t Ap of species A for this reaction 'p' is a function of the reaction rate Kd and of the density nB and is given by (5). And the total relaxation time of the species A for N reactions is (6)(N is the total number of chemical reactions where A species is involved).

Considerin g rection 'p':

In order to see if the electron number density can decrease by recombination, we studied the relaxation time associated to the species. For a given velocity v of particle 'i' we can define 'd' as the mean length or distance that the species can travel before being dissociated.

Where tA is the relaxation time, giving the time characteristic necessary to return to the equilibrium value of the density. With an arbitrary value of the velocity, 'd' gives an idea on the possibilities of the molecules to arrive in the hot regions.

The mean length 'd' is presented in figure 2 versus the temperature for a velocity of 10 m.s-1 for polyatomic species SFX (X=2 to 6), diatomic species (S2, SF, F2) and atomic species (S, F). For the polyatomic species, an increase of the temperature leads to a decrease of 'd'. At 2500 K, the value of 'd' is between 10-8 m and 10-7 m, indicating very fast dissociation of these species. Figure 2 shows that SFX (X=2 to 6) molecules have a low probability of penetrating hot regions (T > 3000 K). The relaxation length d is calculated using a low velocity of 10 m/s ; in real circuit breakers the velocities are much greater than that considered here, so the order of magnitude obtained here for the relaxation length must be weighted by the real velocity. The distance 'd' for diatomic species, which is more stable at high temperatures, is greater than those of polyatomic molecules. The atomic species present greater values, indicating a low dissociation of the species, but regarding in the temperature range 4000 K to 6000 K, the reactions show that the electronic attachment is not important. There are two consequences of this result: first, the effect of convection on the electron density could occur through the diatomic molecules (S2). Secondly, the polyatomic molecule densities should have values near the equilibrium composition.

Figure 2: Mean path of molecules before dissociation in the plasma.