Before Current Zero

In order to investigate the arc behaviour under transient condition, an initial arc conditions need to be chosen in such a way that the arc at current zero should not depend on the chosen initial conditions. A 1000A steady arc has been found to be satisfactory.

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（b）

Figure 4.10 Axial variation of temperature along the central axis at various instants before current zero with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. 1, 1000A; 2, 800A; 3, 600A; 4, 400A; 5, 200A; 6, current zero.

(a)

(b)

Figure 4.11 Axial variation of arc radius along the central axis at various instants before current zero

with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. 1, 1000A; 2, 800A; 3, 600A; 4, 400A; 5, 200A; 6, current zero.

Theoretical investigation has found that under the exit pressure ratio lower than 0.33 which corresponds to an exit pressure of 0.453MPa, the flow field distribution between two electrodes is hardly changed because the exit pressure cannot penetrate into this area. The typical axial

variation of temperature and arc radius along the central axis at various instants which respectively correspond to a current value of 1000A, 800A, 600A, 400A, 200A along with the current zero are presented in Figs. 4.10-4.11.

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(b)

Figure 4.12 Axial variation of electric field along the central axis at various instants before current zero with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. 1, 1000A; 2, 800A; 3, 600A; 4, 400A; 5, 200A; 6, current zero.

For both cases, with the decaying current, the arc radius gradually shrinks with different rates at various axial positions as a result of the accumulated turbulence cooling. With the exit pressure of 0.272MPa, the largest arc radius which appears aftershock moves firstly upstream then downstream near current zero. In contrast, under the exit pressure of 0.680MPa, the axial position where the largest arc radius appears still moves upstream near current zero due to the influence of sucked cold gas.

We can note that the axial temperature in front of the downstream electrode increases when the current decay to a value of 200A under the exit pressure of 0.680MPa. This can be explained that the penetrated pressure shrinks the arc radius near the hollow downstream electrode with sucked gas flow. Regardless of the decaying current, the electric field value near the hollow electrode increase as found in Fig. 4.12 and dominates to bring an increasing current density and hence a rising Ohmic heating density.

(b)

Figure 4.13 Axial variation of pressure along the central axis at various instants before current zero

with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. 1, 1000A; 2, 800A; 3, 600A; 4, 400A; 5, 200A; 6, current zero.

(b)

Figure 4.14 Axial variation of axial velocity along the central axis at various instants before current

zero with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. 1, 1000A; 2, 800A; 3, 600A; 4, 400A; 5, 200A; 6, current zero.

The temperature field distribution is closely connected with the flow field distribution for which the pressure and axial velocity variation as a function of the axial position along the central axis are presented in Figs. 4.13-4.14. Under the exit pressure of 0.680MPa, before the time instant which corresponds to a current of 200A, both the downstream electrode’s blocking effect and the pressure penetration contribute to one shock along the central axis which brings only one velocity decelerations area after shock. Near current zero, these two factors contribute to two velocity decelerations areas as shown in Fig. 4.15. It is noted that the turbulence heat transfer pays an important role in the arc energy dissipation process when current decreases towards zero. The lowest temperature near current zero under the exit pressures of 0.680MPa occurs at the axial position of 51.0mm which locates near the center of the second shock caused by the downstream blocking effect. In this area, the turbulence viscosity and turbulence thermal conductivity is much higher than other parts due to the intense interaction between sucked cold flow and arc. The turbulence-enhanced momentum and energy transport dominates the cooling of SF6 nozzle arcs in these region and leads to a lowest temperature value.

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(b)

Figure 4.15 Temperature and pressure distribution of SF6 arcs in a supersonic nozzle at current zero

with a current decaying rate of 13 A/µs under the exit pressures of (a) 0.680MPa and (b) 0.272MPa. The upper part: temperature; the bottom part: pressure.

Comparing with a supersonic flow before the shock along the central axis with the exit pressure of 0.272MPa, the flow near current zero is subsonic along the whole central axis with the exit pressure of 0.680MPa as presented in Fig. 4.16. The supersonic flow mainly

occurs in the arc’s surrounding regions. For both cases, there exists a stagnation-point in front of the downstream electrode where the gas flow velocity is zero. Due to the weak convective energy exchange in this area, the temperature remains relatively higher than other regions.

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Figure 4.16 Mach number distribution of SF6 arcs in a supersonic nozzle at current zero with a current