**3. Results**

### *3.1. Temperature and Conductivity Dynamics*

Figure 8a,b shows σ contours and the point of the maximum conductivity at 1.35, 2, 2.75, 3.45, and 5 ms in an arc of 200 A. The bright-dark part (green contour) is named core of arc. The rest of the arc inside the red contour is named arc column. The arc light is due to radiation that is proportional to T4. So, the arc column boundary is defined as σ = 1, which is equal to 3300 K but the core is the gliding section of arc (σ > 600, which is similar to 6700 K in air temperature) which is passing more than 80% of the arc current.

Figure 8 shows contours of (a) σ, and (b) the temperature gradient at 1.35, 2, 2.75, 3.45, and 5 ms in an arc of 200 A. It shows that before 2.8 ms the temperature gradient inside the core is high, but after this time it becomes more uniform inside the core center. The point of maximum temperature (*Tmax*) and maximum conductivity is clear in the figures. It is a point with the same color as the related text at the upper left of it. It is close to the moving anode and then shifts to moving cathode but before the CZ falls to the core midpoint. Figure 8d shows that after 2 ms of arc ignition and independent of arc current magnitude, the core is passing 70–80%, and the column is passing around 20–30% of current. The axial centerline of *J* in core shown by the red line is where the *J* gradient perpendicular to the arc column is zero. It is not the spatial centerline, so the core shape and thickness on both sides of the arc center line are not similar due to massive gas flow to the outer sides. Figure 8e shows zero gradient contours for the normal component of current density *Jnorm* (green), σ (red), and temperature (blue) at 1.4 ms. Due to the relatively linear relationship between temperature, σ, and current density in the range of 10–14k K, these contours overlap.

*Energies* **2020**, *13*, 4846

**Figure 8.** (**a**) σ contours and the point of maximum σ, (**b**) Contours of T-gradient at 1.35, 2, 2.75, 3.45, and 5 ms in an arc of 200 *Apeak*, (**c**) Percentage of *Iarc* = *Isource* divided between core/column, (**d**) Electric potential and electric field at 4.5 ms showing anodic and cathodic *Vd*, and (**e**) Zero gradient contours for *Jnorm* (green), σ (red) and *T* (blue) at 1.4 ms on the T-surface.

### *3.2. Simulated vs. Captured Appearance*

Figure 9a displays time-tagged pictures from simulated results of the arc border (outer contour) and core border (inner contour) based on the above definition, including the point of *Tmax* in 200 *Apeak* arc (upper left of *Tmax*). Figure 9b illustrates the arc imaging in FS taken by a 15,000 fps recorder. A dark green filter is used at the camera to prevent saturation, so pictures before 1.57 ms and after 3.37 ms are not so visible. The visual appearance of the curved and the other pulled simulated cores and the core brightness at 2.8 ms (before the change in mode) are confirmed by the experimental results in Figure 10b. Arc current is calculated from:

$$i(t) = I\_{\text{peak}} \times \cos(0.314 \times t \left[\frac{1}{\text{ms}}\right]) \tag{8}$$

A low-frequency (f ≤ 100 Hz) arc on each half-cycle mirrors a direct current arc, the contact separation initiates the arc, and when the current reverses the electrodes interchange their roles as anode or cathode [84]. Simulated and measured arcs are not at the same cycles, so electrode positions are reversed. From Figure 9a, the arc starts with a *Tmax* of 14,790 K on both sides of FS from the sharp points of the contacts. Then it moves downward along the contacts and stays at its bottom because of the intense flow on it. When the arc comes out of the gap between the contacts, its *T* decreases up to 1000 K after 0.25 ms. Then it is elongated, but before 3.6 ms, its temperature is not reduced so much despite the current falling according to Equation (3), and it remains constricted. It is observed that the core is highly compact, hot, and luminous before 2.95 ms, and the arc boundary is more spacious than the core border.

**Figure 9.** (**a**) Time-tagged simulated results of arc and core boundaries for two arcs in series, point of *Tmax* in 200 *Apeak* arc, and (**b**) High-speed imaging with 15,000 fps.

This mode is obvious from high-speed imaging with 15,000 fps in Figure 9b and we call it a constricted mode. At 3.83 ms, the *T* dropped sharply. The position of *Tmax* has been recorded near the moving contact before the mode change, but later it moves to the center of the arc at 4.25 ms. That is, the arc starts to cool on both ends, but the current is not zero yet. We refer to this as a dispersed mode.

**Figure 10.** (**a**) Enlarged image of the arc and (**b**) Its light intensity contours extracted by the image processing vs. simulated arc at 2.8 ms.

An enlarged and horizontally mirrored image of the arc at 2.8 ms is shown in Figure 10a and the light intensity contours [85] extracted by the image processing technics [24] of Figure 10a overlaid on the simulated one are shown in Figure 10b.

### *3.3. Impact of Thermionic Emission*

Thermionic emission acts as a heating source, and it is of crucial importance for contact temperature and ablation simulations, especially for the Cu cathode. The effect of modeling the electron emission from the cathode on the *Tmax* of contacts is compared in Figure 11. "C. Eff." refers to the contact effect and means considering the thermionic emission in simulation. Considering thermionic emission, the temperature of the moving contract does not differ significantly, but as it is shown in Figure 11a the *Tmax* of the fixed cathode increases at 3.4 ms from 707 K in Figure 11b to 1103 K at 1.8 ms, while the *Tmax* of the fixed anode increases from 660 to 800 K. Contact erosion mostly happens near the fixed Cu cathode and then moving Al anode. It was modeled in detail and reported in other recent research [51] and it is also clear from Figure 12a.

**Figure 11.** *Tmax* of contacts (**a**) with thermionic emission modeling, (**b**) Without thermionic emission modeling in 200 *Apeak* arc.

Figure 12a compares the simulated voltage for two 200 A arcs with and without thermionic emission modeling. It reveals that the contact modeling in the first 3.5 ms has no significant effect on *Varc* for two 200 A arcs, but it affects the voltage in the last 1 ms. Anodic and cathodic *Vd*s are modeled in both simulations. Figure 12b shows the melted/ablated points on fixed and moving contacts of the prototype switch. As predicted by the simulations, a trace of arc root is visible on the fixed cathode contact, and the most significant erosion happened at the lower part of the fixed contacts.

**Figure 12.** (**a**) Ablation on fixed and moving contacts (MC in figures means moving contact) and (**b**) Two 200 *Apeak* arcs with(out) thermionic emission modeling.

### *3.4. Arc Mode Change and Interaction of Arcs in Series*

Figure 13 shows the influence of the arc mode change and its effect on increasing the core area. It shows the instantaneous area of the whole arc and its core, as well as the ratio of core-to-column area, for 100 and 200 A arcs with(out) thermionic emission modeling. The slope of the ratio increases suddenly by a factor of 2.15 for 200 A arcs between 2.95 to 3.83 ms, which is the time of change in the arc mode and means the core is not constricted any more. A single 100 A arc is simulated by applying *Jn*(*t*) to one of the fixed contacts. The arc area is smaller, but mode change happens in lower currents.

**Figure 13.** The core area, and the ratio of core-to-column area, for 100 and 200 *Apeak* with(out) thermionic emission.
