Of the very limited experimental results available for direct comparison with theoretical predictions, Frind et al. [3.7], Benenson et al. [3.8] and Frind and Rich [3.9] have reported extensive test results in the form of RRRV for a supersonic nozzle interrupter with fixed upstream (meaning stagnation pressure P0) and
downstream (meaning static pressure at the nozzle exit Pe) pressures.
The experimental conditions of [3.7, 3.8, 3.9] are designed to simulate the current zero period of a two-pressure circuit breaker using a current ramp consisting of a current plateau (DC level) and a linearly decaying current (specified by di/dt) before current zero and a voltage ramp (specified by dV/dt) after current zero. In the experiments, nozzle ablation is avoided by using current levels always below an upper limit of the current with which the arc’s thermal radius is equal to the nozzle
radius (known as the thermal blocking current) [3.7]. The experiments are based on a two-pressure nozzle-electrode configuration as shown in Figure 3.2. Such a two-pressure system eliminates pressure transients caused by wave reflections within a circuit breaker which inevitably affects the arc in the nozzle interrupter. For such a two-pressure system without nozzle ablation we can divide the whole arcing process into a quasi-steady period and a current zero period. The arc behaviour and its thermal interruption capability are investigated by using a current ramp before current zero and a voltage ramp after current zero. Such an approach assumes that peak current does not have effects on arc behaviour during current zero period. This is to assume that the arc at the start of current zero period does not have memory of its previous arcing history. Before current zero period, the arc is in quasi-steady period. Mathematically, an arc will remember its past if the time dependent terms in conservation equations can no long be neglected. When this happens it is considered that the arc is no longer in quasi-steady state. The choice of the plateau of the current ramp is to ensure that the arc at this current does not have memory.
Figure 3.2. Schematic diagram of GE test system used in the experiments of [3.7, 3.8, 3.9]. Stagnation pressure and exit pressures are fixed during arcing.
The assumption of the current zero period being independent of peak arcing current and the absence of pressure transients from other part of a breaker are no longer valid in modern high voltage circuit breakers, e.g. self-blast circuit breakers.
For such breakers, the flow conditions at current zero depend on the whole arcing history. However, the physical processes responsible for arc quenching during current zero period in such breakers are the same as those studied in the experiments of [3.7, 3.8, 3.9]. More importantly, the objective of our investigation is to test the relative merits and applicability of commonly used turbulence models when they are applied to switching arcs. Such tests must be based on the verification of turbulence models by experimental results. It should be noted that all these turbulence models were originally devised for simple flows having a dominant direction of fluid (or gas) motion. Verification on the suitability of turbulence models for switching applications therefore must be based on experimental results obtained under simple flow conditions. To date, the experiments reported in [3.7, 3.8, 3.9] provide the most reliable test data under well defined test conditions. This is the reason why we have chosen to simulate these experimental conditions.
Altogether, arcs in three nozzles, i.e. the nozzle of Frind et al. [3.7], the nozzle of Benneson et al [3.8] and the nozzle of Frind of Rich [3.9], respectively referred to as Nozzle 1, Nozzle 2 and Nozzle 3 hereafter, will be computationally studied in the present investigation. These three nozzles are shown in Figure 3.3, which have different shapes and dimensions as well as electrode configurations. In Figure 3.3, Z=0 indicates the axial position of the nozzle throat. These nozzles have the same expansion half angle (15°) but differ in upstream and throat regions. The throat diameter of Nozzle 2 (12.7 mm) is twice that of Nozzle 1 (6.35 mm). Nozzle 3 is almost the same as Nozzle 2 except that the area variation of Nozzle 3 is continuous.
(a)
(b)
(c)
Figure 3.3. Three nozzle geometries used in the experiments of [3.7, 3.8, 3.9]. Unit of dimensions: mm. (a) Nozzle of Frind et al. [3.7] (Nozzle 1), (b) Nozzle of Benenson et al. [3.8] (Nozzle 2) and (c) Nozzle of Frind and Rich [3.9] (Nozzle 3).
The measured RRRV as a function of stagnation pressure (with P0 ranging from
7.8 atm to 37.5 atm) for the three nozzles are plotted in Figures 3.4(a) and 3.4(b), respectively, for two rates of current decay, di/dt=13 Aμs−1 (13.5 Aμs−1 for Nozzle 3) and 25 Aμs−1 (27 Aμs−1 for Nozzle 3). For Nozzles 1 and 2, the static pressure at the nozzle exit (Pe) is near vacuum in the experiments of [3.7, 3.8] to ensure shock free
inside the nozzle. However, for Nozzle 3, Pe is P0/4 in the experiments of [3.9], for
which the ratio of the nozzle exit pressure to the nozzle upstream stagnation pressure (Pe/P0) is consistent with that normally encountered in a real circuit breaker [3.9]. A
shock can occur inside the nozzle interrupter with such pressure ratio [3.33], which will be shown later by the computational results in Chapters 6 and 7.
(a)
(b)
Figure 3.4. Measured RRRV of an SF6 switching arc for three nozzles given in
Figure 3.3. (a) di/dt=13 Aμs-1 for Nozzles 1 and 2, and di/dt=13.5 Aμs-1 for Nozzle 3 and (b) di/dt=25 Aμs-1 for Nozzles 1 and 2, and di/dt=27 Aμs-1 for Nozzle 3.
The scatters of the measurements are not mentioned in [3.7, .3.8, 3.9]. We therefore evaluate the experimental scatter for the measured RRRV (in terms of percentage difference) at a particular set of discharge conditions by using the following relation:
RRRV RRRV
2 RRRV RRRV scatter al Experiment ignite clear clear ignite (3.37)where RRRVclear is the measured RRRV for thermal clearance as shown in Figure 3.4,
and RRRVreignite is the that for thermal reignition in Figure 3.4. After obtaining the
experimental scatters for individual measurements using the above relation, we can then evaluate the average experimental scatter of the measured RRRV for the range of discharge conditions as shown in Figure 3.4, which is found to be around 40%
The computational results in subsequent four chapters, unless otherwise specified, are obtained under discharge conditions identical with the experiments of [3.7, 3.8, 3.9]. The applicability of turbulence models for prediction of switching arc behaviour will be verified by comparing the computed RRRV with corresponding experimental results given in Figure 3.4.