2.6.2. Turbulent Model

From Figure 5, Re becomes more significant than 10<sup>3</sup> at 0.5ms. This is an indication of TF. So, the algebraic *Y-plus* TF model is used in the first 500 μs of the simulations. Figure 6 shows the arc temperature distributions at different times. The application of the TF model results in lower temperatures and a different shape for arc between contacts (Figure 6d).

**Figure 6.** Arc temperature surface modeled in turbulent flows (TF) at (**a**) 0.15 ms, (**b**) 0.25 ms, (**c**) 0.35 ms, and (**d**) Comparison of arc shape in the laminar and TF model for an arc of 200 *Apeak*.

No large vortices field occurs inside the arc due to a border between the thermal plasma column and TF around it [82]. So, if the mesh is fine enough to resolve the size of the smallest eddies in the flow, the laminar model will remain suitable to reduce the time costs.

### *2.7. The Arc Roots and the Sheath Model*

The simulated temperature distribution in the arc core and the contacts at two different times, 250 μs and 1 ms, are shown in Figure 7a to identify the dominant physical processes inside the arc during different phases of arcing. Up to 250 μs, the arc is sliding in the opposite direction of the moving contact (MC) displacement due to the cold air blowing at the arc column, (see Figure 7c). As it is shown in Figure 7a, in the first 250 μs, the arc length is constant, and the temperature distribution is almost homogenous inside the core, except for the anode and cathode regions. Therefore, the arc-elongating speed is zero before 250 μs.

**Figure 7.** A Core and contacts' temperatures show (**a**) Arc sliding along the contacts up to 0.25 ms, (**b**) Arc elongating between fixed (Fx) and Moving (MC) contacts at the speed of 9 m/s, (**c**) X-position of arc roots vs. time, and (**d**) Temperature, current density, and voltage profile along the contour of *Jmax*.

The arc is not in LTE in these two regions, and the NSE condition is not fulfilled. But simulated results are not so far from the measurements [24]. As it is shown in Figure 7a, arc sliding causes a hot trace at the contacts, which have a temperature range of 600–900 K based on *Tcontact* legend. As it is shown in Figure 7a, the arc temperature is higher than 10k K, i.e., the air is highly ionized, and the NSE assumption is valid. From 1 ms, as it is shown in Figure 7b, the arc is elongating between two points at the contacts. The arc root model is based on [76,83] and the temperature, current density, and voltage profile along the contour of *Jmax* in Figure 7d show the effect of this model.
