INVESTIGATION OF ARC INITIATION IN AN INTERELECTRODE GAP IN WATER BY DISCHARGE OF A HIGH-VOLTAGE CAPACITOR BANK WITH ARC POWER SUPPLIED BY A LOW-VOLTAGE IMPULSE GENERATOR

B. A. FRANKOVSKII, K. A. KHOR’KOV, Yu. G. SHMIGIRILOV

Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering

One method of increasing the energy transmitted from an impulse generator to an arc load in water is to prepare the interelectrode water gap by the discharge of a high-voltage energy source. The conditions for reliable arc transfer and for matching the parameters of the arc channel to the parameters of the stator winding are largely determined by the choice of the voltage and capacitance of the initiating capacitor bank. To ensure reliable transfer of the arc by the impulse generator, prolonged burning of the arc during discharge of the capacitance is desirable. At the same time, owing to the requirements of mobility of the device, restrictions are imposed on the capacitor bank in terms of dimensions and weight.

The transient process in the discharge-circuit chain of the capacitor bank is described by the differential equation

\[ L \frac{di_c}{dt} + r i_c + R_{\mathrm{d}}(t) \cdot i_c + \frac{1}{C}\int_0^t i_c dt = U_0, \tag{1} \]

where \(L, r\) are the total inductance and active resistance of the discharge circuit, equal to the sum of the corresponding parameters of the transmitting coaxial cable, the commutating discharger (trigatron), and the capacitor bank;

\(R_{\mathrm{d}}(t)\) is the nonlinear active resistance of the interelectrode gap of the electrohydraulic radiator (EHR);

\(C\) is the capacitance of the capacitor bank;

\(i_c\) is the discharge current;

\(U_0\) is the initial voltage of the capacitor bank.

To connect the capacitor bank with the EHR, a low-inductance main coaxial cable of type MKPVM-1/30, 30 m long, is used. The capacitor bank is assembled from low-inductance pulse capacitors of type KMK30-10. The voltage amplitude is taken to be 15 kV. In the calculations, the capacitance of the capacitor bank was varied from 5.33 to 53.3 μF in accordance with a change in the bank energy from 600 to 6000 J.

Calculations of the transient process in the discharge-circuit chain were performed on a BESM-4 digital computer. In the calculations, the following parameters of the discharge circuit were adopted, Table 1.

The length of the EHR interelectrode gap was varied from \(l_{\mathrm{e}} = 0.005\) to 0.02 m. At the moment when the high voltage was applied to the EHR electrodes, the resistance of the water interelectrode gap was taken to be

Table 1

equal to 2020 Ω. The mechanism of breakdown of a water-filled interelectrode gap under the action of high voltage consists in the formation and development of leaders up to the bridging of the interelectrode gap by one of them. The resistance of the interelectrode gap in the leader stage (according to V. N. Petrichenko) is determined by the expression

\[ R_{\mathrm{dl}}(t)=\rho_{\mathrm{vn}}-\frac{l_{\mathrm{e}}a}{U^n} \left(\frac{1}{t_1+t_i}+x_0\right), \tag{2} \]

where \(\rho_{\mathrm{vn}}\) is the specific resistance of the interelectrode gap at the moment high voltage is applied to the electrodes; for tap water \(\rho_{\mathrm{vn}}=1.09\cdot 10^3\ \Omega/\text{cm}\);

\(a\) is a constant equal to \(1.06\cdot 10^{10}\ \dfrac{\mathrm{V}^{3.7}\,\text{s}}{\text{cm}}\);

\(U\) is the voltage applied to the electrodes;

\(n\) is the voltage exponent;

\(t_1\) is the time from the moment the voltage is applied to the beginning of leader formation;

\(t_i\) is the time from the beginning of leader formation to the instant under consideration;

\(x_0\) is a correction equal to \(-0.1\cdot 10^{-6}\ \text{s}^{-1}\).

By the time the channel is formed, the resistance of the interelectrode gap turns out to be equal to the values presented in Table 2.

Table 2

The resistance of the arc channel is determined, according to E. V. Krivitskii [1], as

\[ R_{\mathrm{d}}(t)=l_{\mathrm{e}} \sqrt{ \frac{A\,t^{4\alpha(\gamma-1)}} {2\displaystyle\int_0^t i^2\,t^{4\alpha(\gamma-1)}\,dt} }, \tag{3} \]

where \(A=10^5\ \mathrm{V\,s}/\mathrm{m}^2\) is the spark constant,

\(\alpha=0.8\div 1.2\) is a coefficient,

\(\gamma=1.2\div 1.26\) is the effective adiabatic exponent of the plasma in the channel.

Figure 1 presents typical dependences of voltage, current, arc-channel resistance, and energy obtained in the calculation (case \(l_{\mathrm{e}}=0.02\ \text{m}\), \(W_0=600\ \text{J}\)). For comparison, Fig. 2 presents

Fig. 1. Curves of the variation of the arc voltage \(U_d\), current \(i_c\), resistance of the arc channel \(R_d\), and energy introduced into the arc \(W_d\)

Fig. 2. Oscillograms of the arc voltage and current during discharge of a capacitance with an energy reserve of 600 J into an interelectrode gap of 0.02 m

oscillograms of voltage and current obtained on the experimental setup for the same values of the circuit parameters. The calculation results agree satisfactorily with the experimental data. In Fig. 1 the proposed instant of switching the impulse generator onto the arc gap is denoted by the index \(t_v\). The takeover of the arc by the generator must take place during the time \(t_p\), when the generator and the capacitance operate jointly. As the discharge of the capacitor bank decays, the active resistance of the arc channel increases somewhat in comparison with the minimum value that occurs when the discharge current reaches its maximum.

It is convenient to characterize the magnitude of the active resistance of the arc channel during the arc-takeover time by the mean value of the resistance over this time interval, denoted by \(R_{p\,\mathrm{av}}\) [2].

The energy introduced into the discharge channel is determined as the sum of the mean values at each calculation step

\[ W_d=\sum_{i=1}^{n}\frac{\Delta t}{8}\,[i_c(t_i)+i_c(t_{i+1})]^2\cdot [R_d(t_i)+R_d(t_{i+1})]. \tag{4} \]

The plot of energy (Fig. 1) reflects the stepwise introduction of energy into the discharge channel. Each step corresponds to its own half-period of the discharge current. The transfer of energy into the arc channel is significant only during the first three half-periods of the discharge.

The results of the computer calculation have been processed and are presented in Tables 3–6.

The following parameters are given in the tables:

\(I_{m1}\) — amplitude of the discharge current of the first half-period;
\(R_{\mathrm{d\,min}}\) — minimum resistance of the formed discharge channel;
\(t_m\) — instant of time corresponding to \(R_{\mathrm{d\,min}}\);
\(U(t_m)\) — voltage across the arc at time \(t_m\);
\(W(t_m)\) — energy introduced into the discharge channel by time \(t_m\);
\(\tau_c\) — duration of the capacitor-bank discharge;
\(W(\tau_c)\) — total energy introduced into the discharge channel;
\(R_{\mathrm{d}}(\tau_c)\) — resistance of the discharge channel at time \(\tau_c\);
\(R_{\mathrm{d\,eqv}}\) — average resistance of the discharge channel for \(t > t_m\);
\(t_n\) — time of joint operation of the impulse generator and the capacitor bank;
\(\eta\) — efficiency of the capacitor bank, equal to the ratio

\[ \frac{W(\tau_c)}{W_0}. \]

Table 3

Interelectrode gap \(l_{\mathrm{e}} = 0{,}02\ \mathrm{m}\)

Table 4

Interelectrode gap \(l_{\mathrm{e}} = 0{,}015\ \mathrm{m}\)

Table

Interelectrode gap \(l_e = 0.01\ \text{m}\)

Table 6

Interelectrode gap \(l_e = 0.005\ \text{m}\)

Fig. 3. Change in arc resistance at different energies of the capacitor bank for 1) \(l_e=0.02\ \text{m}\); 2) \(l_e=0.015\ \text{m}\); 3) \(l_e=0.01\ \text{m}\); 4) \(l_e=0.005\ \text{m}\).

Figure 3 presents curves of the variation of the mean arc resistance \(R_{\mathrm{d,eq}}\) as a function of the initial energy, for various interelectrode gaps of the IPG.

In the highlighted (hatched) range, the resistance \(R_{\mathrm{d,eq}}\) corresponds to the range of matching between the parameters of the generator and the arc. The discharge duration of the capacitor bank, at a constant interelectrode-gap length, increases with increasing initial charge of the bank.

Fig. 4. Dependence of the discharge duration on the energy of the capacitor bank for
1) \(l_{\mathrm{e}}=0.02\ \mathrm{m}\);
2) \(l_{\mathrm{e}}=0.015\ \mathrm{m}\); 3) \(l_{\mathrm{e}}=0.01\ \mathrm{m}\);
4) \(l_{\mathrm{e}}=0.005\ \mathrm{m}\)

Figure 4 presents the dependence of the time \(t_n\) on the energy of the capacitor bank \(W_0\) for various interelectrode gaps \(l_{\mathrm{e}}\).

Thus, as a result of calculating the transient process in the discharge circuit of the initiating high-voltage capacitor bank, important characteristics of the initiated interelectrode gap have been found, namely \(R_{\mathrm{d,eq}}\) and \(t_n\), which are necessary for analyzing the conditions for arc takeover by the impulse generator. Curves have been obtained from which one can choose the required energy of the capacitor bank in order to ensure optimal values of \(R_{\mathrm{d,eq}}\) and \(t_n\). It is shown that the mean resistance of the arc channel can be brought to the level of the total supertransient resistance of the impulse generator, on the order of \(0.05\ \Omega\), while the capacitance discharge time can be brought to \(300 \div 500\ \mu\mathrm{s}\), sufficient for reliable arc takeover by the impulse generator. In this case, the energy stored in the initiating capacitor bank does not exceed \(1\%\) of the energy that the impulse generator must supply.

REFERENCES

1. E. V. Krivitskii, “Investigation of the resistance of an underwater spark-discharge channel,” Journal of Technical Physics, Vol. 40, No. 11, 1972.

2. I. Z. Okun, “Investigation of the electrical characteristics of a pulsed discharge in a liquid,” Journal of Technical Physics, Vol. 39, No. 5, 1969.