Operation of a Sinusoidal Voltage Source on an Arc in Water
Abstract Generated abstract
The paper examines the use of a sinusoidal voltage source for producing an underwater arc initiated by an exploding wire, with attention to electrohydraulic pulse generation and the resulting pressure wave. It develops the relevant electrical considerations for generator voltage, current, inductive reactance, and energy input, then reports experiments using a 50 Hz transformer source, copper wire bridges of varied geometry, controlled switching angle, and oscillographic measurements of current, voltage, resistance, and pressure. The results indicate that the pressure pulse has distinct optima with respect to wire length and switching angle, including a maximum near a 40 mm wire length for the tested 0.83 mm wire and near 36 degrees for a 0.72 mm by 32 mm wire. The study concludes that effective operation requires matching the source internal resistance to the interelectrode gap resistance during the arc stage.
Full Text
Proceedings
of the Tomsk Order of the October Revolution
and Order of the Red Banner of Labor
Polytechnic Institute named after S. M. Kirov
Volume 301
1975
OPERATION OF A SINUSOIDAL VOLTAGE SOURCE ON AN ARC IN WATER
B. A. Frankovsky
(Presented by the scientific seminar of the Departments of Electrical Machines
and General Electrical Engineering)
The choice of one or another energy source for nonstationary electrohydraulic installations is determined by its mobility and by its technical capabilities from the standpoint of obtaining the required energy values, the repetition frequency of the generated pulses, and the hydrodynamic characteristics of the elastic pressure wave.
Existing electrohydraulic installations intended for exciting seismic oscillations, created on the basis of capacitor banks, have a current-pulse duration in the arc on the order of \(10^{-4}\) sec. When the arc is supplied from a shock generator, the duration of arc burning increases by an order of magnitude, owing to which one should expect an increased amplitude of the low-frequency components \((10 \div 300\ \text{Hz})\) in the frequency spectrum of the generated elastic pressure pulses.
The efficiency of converting the electromagnetic energy of such an installation will be higher the greater the percentage of low-frequency components in the formed elastic pressure wave.
The process of electrical breakdown of the liquid and the formation of the arc channel, on the one hand, are determined by the generator voltage
\[ U = 4{,}44\, w_1 k_{w1} f \Phi, \tag{1} \]
where \(f\) is the frequency of the sinusoidal voltage of the generator;
\(k_{w1}\) is the winding factor of the stator winding;
\(\Phi\) is the main flux of the machine;
\(w_1\) is the number of turns of the generator stator winding.
This process presents no difficulty only in the case of the use of high voltages.
On the other hand, the greatest amplitude of the current in the arc
\[ I_{\mathrm{ud}} = \frac{1{,}8 \cdot 1{,}05 \sqrt{2}\, U}{x_{\mathrm{ud}}} \tag{2} \]
occurs at the smallest value of the shock inductive reactance of the generator
\[ x_{\mathrm{ud}} = \omega k \lambda'' w_1^2, \tag{3} \]
where \(\lambda''\) is the equivalent permeance of the generator in the supertransient regime, taking into account the influence of the field-winding circuits and the rotor damping system;
\(\omega\) is the angular frequency of the generator emf;
\(k\) is the proportionality coefficient.
The amount of energy introduced into the arc, with matched resistance \(R_{\mathrm{d}}(t)\), is determined by the square of the current
\[ W_{\mathrm{d}}=\int_{0}^{t} i_{y\mathrm{d}}^{2}\cdot R_{\mathrm{d}}\,dt . \tag{4} \]
Thus, pulse generators for electrohydraulic installations must be designed for large currents, which is ultimately achieved by reducing the number of turns of the stator winding. The latter causes a decrease in the generator voltage; consequently, there arises the need for preliminary initiation of the interelectrode water gap by auxiliary means. The most effective initiation of the arc is carried out with the aid of exploding wires (wire bridges). A pulse generator connected to an exploding wire, up to the moment of its explosion, accumulates electromagnetic energy in the leakage fields of the stator winding. From the moment the arc is formed, the generator transfers to the arc both the electromagnetic energy of the leakage fields and the converted kinetic energy of the rotor.
The duration and magnitude of the energy introduced into an arc initiated by a wire can be regulated both by selecting the geometrical parameters of the exploding wire and by changing the initial angle at which the generator is switched onto the wire.
The criterion for optimum operation of the pulse generator on the wire is the maximum values of the amplitude and duration of the compression pulse. It is known that the compression pulse is formed under the action of two factors [1, 2]: directly by the electrical explosion of the wire and by the arc stage.
In the present work, the problem of optimizing the circuit is solved empirically—by selecting the diameter and length of the wire and by changing the initial angle at which the generator is switched on.
In carrying out the experiments, the source of sinusoidal voltage was a 560 kVA transformer fed from the municipal electric grid. The energy source used serves as a model of an energy unit with a pulse generator, since it has the same frequency and similar voltage and current waveforms.
The basic electrical circuit of the setup is shown in Fig. 1. The electrodes, connected by wire 2, are placed in a special tank 3 filled with tap water. At a distance of 100 mm
Fig. 1. Basic electrical circuit of the experimental setup: 1 — controlled switching device; 2 — exploding wire; 3 — tank; 4 — pressure sensor; 5 — shunt; 6 — voltage divider; 7 — coaxial measuring cable; 8, 9 — first and second pair of plates of the S1-16 oscillograph; 10 — S1-29 oscillograph.
from the center of the wire normally to its axis. A pressure sensor 4 is installed. From a sinusoidal voltage source ($U=220$ V and $f=50$ Hz), one half-wave of the “extra” current is fed to the wire by means of the controlled valve switching device 1.
The recording system contains oscillographs 8 and 9 of type S1-16, intended for oscillographing current and voltage; oscillograph S1-29 10 for recording the pressure pulse; a transmitting path made with shielded coaxial cable RK-75 7; a shunt 5 of type 75 ShSM (75 mV, 150 A); a voltage divider 6 made with noninductive TVO resistors with divider ratio $K=0.0034$; and pressure sensor 4.
In the pressure sensor, a barium titanate tablet 8 mm in diameter and 4 mm thick was used as the sensitive element. Reflection of the elastic wave from the end faces of the cylindrical piezoelement was eliminated by connecting it to a long rod of the same cross section and with the same acoustic resistance as that of the sensitive element. The piezoelement and the rod are placed in a brass tube, which serves as a frame and as shielding against electromagnetic pickups during the explosion of the conductor.
A study of the influence of the wire parameters, in order to identify the relationship between the energy characteristics ($W_{\mathrm{p}}$—total energy released in the wire, J; $W_{\mathrm{v}}$—volume energy density, kJ/cm$^3$) and the hydrodynamic characteristic of the pressure pulse ($P_{\mathrm{m}}$—pressure-pulse amplitude), was carried out for copper wires of diameters 0.51, 0.69, and 0.83 mm while varying their length within the range 20–110 mm. In analyzing the influence of the initial switching angle within the range from 0 to 90°, a wire 0.72 mm in diameter and 32 mm long was used.
The experiments showed that explosion of a wire 0.51 and 0.69 mm in diameter generates a compression pulse of smaller amplitude than explosion of a wire 0.83 mm in diameter when the explosion occurs at the current maximum. The experimental results for wires 0.72 mm and 0.83 mm in diameter are summarized in Tables 1 and 2, where $l_{\mathrm{n}}$ is the wire length, mm; $d_{\mathrm{n}}$ is the wire diameter, mm; $I_{\mathrm{m}}$ is the current-pulse amplitude, kA; $t_{\mathrm{v}}$ is the time of energy accumulation in the wire before explosion, s; $W_{\mathrm{p}}$ is the total energy introduced into the wire, J; $W_{\mathrm{v}}$ is the energy accumulated in the wire before explosion, J; $W_{\mathrm{v}}$ is the volume energy density, kJ/cm$^3$; $\Psi$ is the initial switching angle of the sinusoidal voltage source onto the wire, deg; $P_{\mathrm{m}}$ is the amplitude value of the elastic pressure pulse, relative units (rel. units).
Table 1
| $l_{\mathrm{n}}$, mm | $I_{\mathrm{m}}$, kA | $t_{\mathrm{v}}\cdot 10^{-3}$, s | $W_{\mathrm{p}}$, kJ | $W_{\mathrm{v}}$, kJ | $W_{\mathrm{v}}$, kJ/cm$^3$ | $P_{\mathrm{m}}$, rel. units |
|---|---|---|---|---|---|---|
| 30 | 3.85 | 6.00 | 2.511 | 1.792 | 150 | 3.10 |
| 40 | 4.40 | 5.50 | 2.250 | 1.733 | 93 | 3.55 |
| 50 | 4.51 | 5.50 | 2.097 | 1.638 | 62 | 2.49 |
| 60 | 4.18 | 4.75 | 2.004 | 1.746 | 48 | 1.85 |
| 70 | 4.51 | 4.50 | 2.070 | 1.778 | 55 | 1.70 |
| 80 | 4.40 | 5.00 | 2.240 | 1.809 | 54 | 1.45 |
| 90 | 4.72 | 5.00 | 2.432 | 1.815 | 52 | 1.30 |
| 100 | 4.62 | 4.50 | 2.598 | 1.801 | 47 | 1.30 |
| 110 | 4.50 | 5.50 | 2.704 | 1.950 | 38 | 1.30 |
Table 2
| \(I_m\), kA | \(t_b \cdot 10^{-3}\), s | \(W_n\), kJ | \(W_b\), kJ | \(W_v\), kJ/cm | \(\psi\), deg | \(P_m\), rel. units |
|---|---|---|---|---|---|---|
| 3.20 | 5.25 | 2.774 | 0.429 | 210 | 18 | 1.83 |
| 3.33 | 4.60 | 1.984 | 0.212 | 155 | 36 | 2.97 |
| 3.33 | 5.00 | 1.720 | 0.284 | 138 | 45 | 2.71 |
| 3.24 | 5.30 | 1.560 | 0.236 | 122 | 54 | 2.34 |
| 3.15 | 6.0 | 1.269 | 0.227 | 98 | 72 | 1.74 |
Fig. 2. Oscillograms of the current and voltage during explosion of a copper wire (\(l_n = 32\) mm and \(d_n = 0.72\) mm) at an initial switching angle of the sinusoidal source of \(36^\circ\).
Figure 2 shows characteristic oscillograms of the current and voltage during the explosion of copper wires (\(l_n = 0.72\) mm, \(d_n = 32\) mm) and a source switching angle of \(36^\circ\). Oscillograms of the current and voltage for other lengths and diameters of the exploding wire are of a similar character and are not presented. From the current and voltage oscillograms it is possible to record four stages in the development of the process: accumulation of energy in the wire, explosion, a sharp decrease in current, and the arc stage.
The accumulation in the wire of the energy required for the phase transformation occurs, on average, over \(5 \cdot 10^{-3}\) s. By the end of this time the conductor breaks up into small parts, local regions with reduced conductivity appear, and the current in the conductor decreases smoothly. In the regions with reduced conductivity, intense energy release takes place. When the energy reaches the threshold value \(W_{\text{th}}\) required for the phase transformation in the local regions of the conductor, the wire explodes. As can be seen from the oscillogram in Fig. 2, the explosion of the wire is accompanied by a sharp drop in the current to some minimum value close to zero, which corresponds to an instantaneous decrease in conductivity.
A sharp drop in the current in a circuit with large inductance is accompanied by a surge of self-induction emf (Fig. 2, lower curve), exceeding the amplitude value of the source voltage by more than a factor of 4. With a comparatively small emf, not exceeding \(1.5\ \mathrm{kV}\), interelectrode gaps of up to \(150\ \mathrm{mm}\) are broken down.
The arc stage is characterized by a constant value of the voltage (Fig. 2) and by the formation of a vapor-gas bubble—the source of an elastic compression wave—whose dimensions depend on the magnitude and duration of the flowing current.
The energy released in the wire \(W_n\), the volumetric energy density \(W_v\), and the pressure developed \(P_m\), as functions of the wire length \(l_n\) and the initial switching angle \(\Psi\), are presented, respectively, in Figs. 3 and 4. The pressure curves \(P_m\) have a clearly expressed extremum. In Fig. 3 the extremum is determined by the optimal wire length, equal to \(40\ \mathrm{mm}\), while in Fig. 4 it is determined by the initial switching angle \(36^\circ\) for fixed geometrical parameters of the wire.
Fig. 3. Energy released in the wire (curve 1), volumetric energy density (curve 2), and developed pressure (curve 3) as functions of its length at constant diameter and \(\psi = 0\). \(I\) — specific energy of copper sublimation.
An oscillogram of the pressure pulse is shown in Fig. 5. Fig. 6 shows characteristic changes in the resistance of exploding wires over time, obtained by processing oscillograms of current and voltage.
The resistance curves of exploding wires at different initial switching angles of the sinusoidal source have an identical form. In the stage of energy accumulation, the resistance of the wires is-
Fig. 4. Energy released in the wire (curve 1), volumetric energy density (curve 2), and the pressure developed (curve 3) as functions of the switching angle of the sinusoidal source, for constant geometric dimensions of the wire.
1 — specific sublimation energy of copper.
Annotations in the figure: \(d = 0.72\ \mathrm{mm}\), \(l_{\mathrm{п}} = 32\ \mathrm{mm}\); horizontal axis: \(\psi\), deg.; vertical scales include \(W_{\mathrm{п}}\), J; \(p_m\), rel. units; \(W_v\), kJ/cm\(^3\).
Fig. 5. Oscillogram of the pressure pulse from the explosion of a wire \((l_{\mathrm{п}} = 32\ \mathrm{mm}\) and \(d_{\mathrm{п}} = 0.72\ \mathrm{mm})\) at an initial switching angle of the sinusoidal source of \(18^\circ\).
Annotation in the figure: \(2\ \mu\mathrm{s}\).
changes only slightly and may be regarded as constant. At the moment of explosion of the conductor, the resistance of the interelectrode gap increases by more than an order of magnitude. In the established arc stage, the minimum resistance is higher than the resistance of the wire in the accumulation regime. By the end of the current pulse, the resistance rises sharply.
Thus, the experiments carried out showed the necessity of matching the internal resistance of the power source with the resistance of the interelectrode gap in the arc stage.
Fig. 6. Change in the resistance of the exploding wire over time: 1 — \(d_p = 0.83\) mm, \(l_p = 40\) mm, \(\psi = 0\); 2 — \(d_p = 0.72\) mm, \(l_p = 32\) mm, \(\psi = 36^\circ\).
REFERENCES
- V. A. Borotkov, G. A. Nesvetailov. “Physics of Combustion and Explosion,” 1970, No. 2, vol. 6.
- F. Hammon. Zeitschrift für Angewandte Physik. 31, 2, 1971.