APPARATUS FOR STUDYING THE EXPLOSIBILITY OF MIXTURES

M. A. MELNIKOV, A. A. DULZON, B. M. KOVALCHUK, Yu. A. KOTOV

(Presented by the scientific seminar of the Research Institute of High Voltages and the Department of High-Voltage Engineering.)

It is known that a number of branches of industry (coal, chemical, petroleum, gas, etc.) are characterized by the explosibility of the production atmosphere. Under these conditions, electrical sparking arising when the contacts of various electrical devices used in production premises are switched, or discharges of static electricity formed in certain technological processes, may cause dangerous ignition of an explosive mixture of gas or vapor with air. For this reason, the question of what is the minimum value of the energy of an electrical discharge capable of igniting an explosive mixture is of considerable interest from the standpoint of ensuring safety in coal mines, in production facilities for obtaining synthetic rubber and plastics, in oil refining, and so on.

To solve the question of work safety under these conditions, studies are needed in order to determine the minimum value of the spark energy that causes ignition and explosion of mixtures of various concentrations, the influence of the magnitude of the generating capacitance, voltage, spark duration, number of pulses, and their repetition frequency on the processes of ignition and explosion of the mixture.

To carry out this set of studies, we have developed and constructed a special apparatus.

In the present work we shall consider the features of some of its units, the method of taking into account the errors introduced by the measuring circuits when calculating the energy released in the spark from oscillograms of current and voltage, as well as the features of the adopted circuits for producing a spark and recording voltage and current during the discharge of a capacitance varying within the limits of 15 nF–10 μF, charged to a voltage of (8–0.5) kV in single and multiple (with a repetition frequency up to 1 kHz) processes.

Choice of circuits for producing the spark, recording voltage and current, and synchronization

When recording single and multiple processes with an oscilloscope with triggered sweep, two synchronization circuits are possible in principle.

In the first variant, the oscillograph is triggered by an auxiliary voltage pulse which subsequently, after a time equal to the triggering time of the oscillograph, causes the phenomenon under study to appear.

In the second variant, the oscillograph is triggered by a voltage pulse obtained during the process under study, while the voltage characterizing this process is applied to the deflection plates through a delay line. The delay time of the line is chosen equal to or greater than the triggering time of the oscillograph.

To record the voltage at the spark gap located in the gas mixture under study, the following synchronization circuits were considered.

Fig. 1. Electrical circuit for synchronizing and measuring the voltage at the spark gap.

Circuit 1, Fig. 1a. The generating capacitance \(C_{\mathrm{g}}\) is charged from the power supply \(I.\ P.\) to a voltage close to the breakdown voltage; then a voltage pulse, produced by the discharge of the capacitance \(C_{\mathrm{p}}\) through the contacts of a high-voltage relay into the cable, was applied to the spark gap \(P_1\) through line \(L_1\) (RK-1 cable 75–150 m long). The gap \(P_1\) breaks down, and the ultraviolet radiation in it causes breakdown of the gap under investigation, \(P_2\).

The oscillograph was triggered by a voltage pulse from the resistance \(R_1\). The phenomenon was recorded by means of a capacitive voltage divider \(C_1, C_2\), with the capacitance \(C_2\) serving as the deflection plates of the oscillograph tube.

The work was carried out on OK-17 and DESO-1 oscillographs. The following results were obtained:

1. The circuit operates stably (the phenomenon arriving at the oscillograph has a scatter of \(1/4\) of the screen):

a) with a minimum distance between the gaps \(P_1\) and \(P_2\) equal to \(0.5\) cm,

b) with large currents in the gap \(P_1\) (capacitance \(C_{\text{p}} = 0.25\ \mu\text{F}\), \(U_{\text{sp}} = 3\ \text{kV}\), \(I_{p_1} = 80\ \text{A}\)),

c) the voltage \(U\) at the spark gap \(P_2\) must be as close as possible to the breakdown value \((0.9—0.95)\,U_{\text{p}}\),

1. with short gaps \((U_{\text{pr}} = 0.6—1.2\ \text{kV})\) the stability of operation deteriorates sharply (is practically absent),

2. the presence of quartz glass, 3 mm thick, between the gaps \(P_1\) and \(P_2\) makes operation with the circuit possible for the given gaps \((3—5\ \text{kV})\) at sweep times of not less than \(100\ \mu\text{s}\).

Circuit 2, Fig. 1b. The voltage at the investigated gap \(P_2\) appears after breakdown of the gap \(P_1\), made in the form of a trigatron. Voltage recording is carried out in the same way as in circuit 1. The oscillograph is triggered by a voltage pulse obtained across the resistance \(R_1\) when the capacitances \(C_{\text{p}}\) and \(C_3\) discharge into cable \(L_1\). The delay in the operation of the trigatron is caused by transmission of the igniting pulse through cable \(L_1\), whose delay is equal to the operating time of the oscillograph. The instability in this synchronization circuit is due to the scatter of the breakdown voltages in the gaps \(P_1\) and \(P_2\).

Fig. 2a. Block diagram for recording phenomena with a DESO-1 oscillograph.

The investigations carried out showed that the circuit operates stably at sweep times of \(15—20\ \mu\text{s}\), with precise adjustment of the gap \(P_1\), the voltage across which must be \(0.9—0.95\,U\) of the breakdown value. Ultraviolet illumination of the gap \(P_2\) is desirable.

Circuit 3, Fig. 2a. In this circuit the synchronizing pulse is formed in the input stage of the DESO-1 oscillograph upon breakdown of the investigated spark gap. The triggering pulse, after preliminary amplification, is fed to the sweep generator.

The investigated phenomenon, through delay lines, is delivered for subsequent amplification to the amplification stages, and then to the plates of the tube. The delay lines provide a delay equal to the operating time of the oscillograph.

As a result of the investigations carried out on circuits for obtaining a spark in a gap located in the investigated gas mixture, and for recording voltage and current in the spark gap, the third circuit was adopted for implementation for the following reasons:

1. In this circuit there is only the investigated spark gap. The energy stored in the capacitor is released in one gap.

the gap. This makes it possible to measure the energy released in the spark gap, from the initial and residual voltage and the known generating capacitance, i.e., to duplicate the oscillographic measurements.

1. This circuit makes it possible to record the phenomenon at times of 0.3–1000 μsec, whereas the first two circuits raise the lower limit to tens of μsec.

2. Recording according to the third circuit, using broadband amplifiers, makes it possible to dispense with active shunts for recording the current and to use a magnetic belt, i.e., to have no electrical connection with the circuit under investigation.

3. The circuit makes it possible not to use the ultraviolet illumination required in the first circuit and desirable in the second, which may affect the explosibility of the mixtures under investigation.

Fig. 2b. Electrical circuit of the synchronization and current- and voltage-measurement unit in the spark gap:
\(C_g\)—generating capacitance,
\(L_p\)—inductance in the discharge circuit,
\(C_1\)—capacitance of the high-voltage arm of the voltage divider.
\(R_1\)—input resistance of the amplifier.
\(R_g\)—damping resistance,
\(L_p\)—inductance of the belt,
\(R_p\)—resistance of the ohmic shunt.

1. The third circuit is a rigid-synchronization circuit. The scatter in the appearance of the phenomenon on the screen is due only to the scatter in the triggering of the oscilloscope circuit, which is practically absent.

Each breakdown of the gap is recorded by an oscilloscope. Detuning of the gap by voltage is eliminated.

1. The use of amplifiers with an adjustable gain makes it possible, over wide ranges, to measure voltage and current using the same dividers and shunts, i.e., the error that arises when changing from one sensor to another is eliminated.

2. The circuit is suitable for recording single and repeated processes.

The input stages of the current-measurement units (together with the belt) and of the voltage-measurement units (with the divider) are placed in metal shields.

Features of Current Measurement with a Magnetic Belt

When using a magnetic belt with a frame made of insulating material and measuring the current in the belt \(i_p\) by means of a shunt \(R_{\mathrm{sh}}\), the following conditions must be fulfilled:

1. The time constant of the belt winding, \(\dfrac{L}{R_{\mathrm{p}}+R_{\mathrm{sh}}}\), must not be reduced to values comparable with the time constant characterizing the shape of the current being measured.

2. The belt current

\[ i_{\mathrm{p}}=\frac{i}{w}, \tag{1} \]

where \(w\) is the number of turns of the belt.

1. The inductance of the belt

\[ L=\mu_0 S \frac{w^2}{l}, \tag{2} \]

where \(S\) is the cross section of the belt, and \(l\) is the length of the mean line of the belt.

1. The voltage drop across the shunt, \(i_{\mathrm{p}}R_{\mathrm{sh}}\), measured with an oscilloscope, must vary within limits that make it possible to carry out oscillography with the greatest accuracy.

When the current \(i\) in the discharge circuit is reduced, the fourth condition is not fulfilled; decreasing \(w\) will lead to an increase in \(i_{\mathrm{p}}R_{\mathrm{sh}}\), but according to condition (2) the inductance of the belt will decrease, and this in turn will lead to violation of the first condition.

Thus, the possibilities of using a magnetic belt with a frame made of insulating material for current measurement are limited by the minimum values of the current. Increasing the inductance of the belt by using an alsifer core makes it possible to extend the measurement limits of the belt current toward smaller current values.

The regions of application of a magnetic belt with an alsifer core were established experimentally.

Some experimental results are given in Table 1.

Table 1

For comparison, data for a belt with a frame made of insulating material are also given here.

The maximum current measurement limit of each belt was established from the condition that the vertical deflection on the oscilloscope screen not exceed 30 mm, since within this deflection, according to the instructions for the S1-7 oscilloscope and our verification, the gain factor of the amplifier varies linearly. Thus, with a belt having an alsifer core, currents on the order of tenths of an ampere can be measured.

Calculation of the Voltage-Recording Circuit

The voltage across the spark gap is recorded by means of the circuit shown in Fig. 2b (lower).

The equivalent circuit for calculating the voltage recorder is shown in Fig. 3, where \(U_{C0}\) is the initial voltage on \(C_1\), and \(U\) is the voltage across the spark gap, determined by the current of the measuring circuit and the generator.

The calculation was performed by the operational method [1].

For this circuit

\[ U_{R_1}=I(P)\cdot \frac{\dfrac{R_1}{C_2P}}{R_1+\dfrac{1}{C_2P}} =I(P)\frac{R_1}{1+R_1C_2P}, \tag{1} \]

\[ I(P)= \frac{U_{c_0}+U}{\dfrac{1}{C_1P}+\dfrac{R_1}{1+R_1C_2P}} = \frac{(U_{c_0}+U)C_1P(1+R_1C_2P)} {1+R_1C_2P+R_1C_1P}. \tag{2} \]

Fig. 3. Equivalent circuit when recording the voltage across the spark gap (designation the same as in Fig. 2b).

Fig. 4. Equivalent circuit when recording the voltage across the spark gap with damping resistance \(R_3\) connected.

Solving equations 1, 2, we obtain

\[ U_{R_1}(P)= \frac{(U_{c_0}+U)C_1P(R_1C_2P+1)\cdot R_1} {(R_1C_2P+1+R_1C_1P)(R_1C_2P+1)} = \frac{(U_{c_0}+U)R_1C_1P} {R_1C_2P+1+R_1C_1P} = \frac{N(P)}{M(P)}. \]

We determine \(p\)

\[ (R_1C_2+R_1C_1)P+1=0, \]

\[ P=-\frac{1}{R_1C_2+R_1C_1} =-\frac{1}{R_1(C_2+C_1)}, \]

for \(P=0\), \(N(P)=0\); therefore the constant term in the expansion will be absent. \(M'(P)=R_1C_2+R_1C_1\). Then, by the expansion theorem,

\[ U_{R_1}(t)= \frac{(U_{c_0}+U)R_1C_1P}{R_1(C_2+C_1)P}\cdot e^{pt} = \frac{(U_{c_0}+U)R_1C_1}{R_1(C_2+C_1)} \cdot e^{-\frac{1}{R_1(C_2+C_1)}t} = \]

\[ = \frac{(U_{c_0}+U)C_1\cdot e^{-\frac{t}{R_1(C_1+C_2)}}} {C_1+C_2}, \]

whence

\[ U=\frac{U_{R_1}}{\dfrac{C_1}{C_1+C_2}\cdot e^{-\dfrac{t}{R_1(C_1+C_2)}}}-U_{c_0}. \]

Let us assume that

\[ \frac{C_1}{C_1+C_2}=\frac{1}{k}; \qquad k=\frac{C_1+C_2}{C_1}, \]

\[ U=\frac{U_{R_1}\cdot k}{e^{-\dfrac{t}{R_1(C_1+C_2)}}}-U_{c_0}. \]

It is evident from the formula that, for \(e^{-\dfrac{t}{R_1(C_1+C_2)}}\approx 1\), the voltage across the spark gap can be calculated from the obtained oscillogram and the known \(U_{c_0}\).

The error introduced by the recording circuit is equal to zero at \(t=0\) and increases as the duration of the recorded process increases; moreover, it can be determined for each specific case.

Under real conditions, because of the ultrahigh frequencies that arise during the discharge, it becomes necessary to include the damping resistance \(R_2\) in the measuring circuit.

The circuit for recording the voltage with a damping resistance is shown in Fig. 4a. The equivalent recording circuit, taking into account the damping resistance, is shown in Fig. 4b. For this circuit we have:

\[ I(P)= \frac{U_{c_0}+U} {R_2+\dfrac{1}{C_1P}+\dfrac{\dfrac{R_1}{C_2P}}{R_1+\dfrac{1}{C_2P}}} = \frac{(U_{c_0}+U)(R_1C_2P+1)C_1P} {(R_2C_1P+1)(R_1C_2P+1)+R_1C_1P}. \tag{1} \]

\[ U_{R_1}(P)=I(P)\, \frac{\dfrac{R_1}{C_2P}}{R_1+\dfrac{1}{C_2P}} = I(P)\frac{R_1}{R_1C_2P+1}. \tag{2} \]

Substituting the value of \((P)\) from equation (1) into (2), we obtain

\[ U_{R_1}(P)= \frac{R_1C_1P(U_{c_0}+U)} {R_1C_1R_2C_2P^2+(R_1C_2+R_1C_1+R_2C_1)P+1} = \frac{N(P)}{M(P)}, \]

where

\[ P_{1,2}= \frac{ -(R_1C_2+R_2C_1+R_1C_1) \pm \sqrt{(R_1C_2+R_1C_1+R_2C_1)^2-4R_1C_1R_2C_2} } {2R_1C_1R_2C_2} \tag{3} \]

for \(P=0\), \(N(P)=0\); the constant term of the expansion is absent.

\[ M'(P)=2R_1C_1R_2C_2P+R_1C_2+R_1C_1+R_2C_1. \]

By the expansion theorem we have:

\[ U_{R_1}(t)=\frac{N(0)}{M(0)}+\sum_{n=1}^{n=\kappa}\frac{N(P_\kappa)}{M'(P_\kappa)P_\kappa}= \]

\[ =\frac{R_1 C_1 P_1 (U_{c_0}+U)\cdot e^{p_1 t}} {(2R_1 C_1 R_2 C_2 P_1+R_1 C_1+R_1 C_2+R_2 C_1)\cdot P_1}+ \]

\[ +\frac{R_1 C_2 P_2 (U_{c_0}+U)} {(2R_1 C_1 R_2 C_2 P_2+R_1 C_1+R_1 C_2+R_2 C_1)\cdot P_2}\cdot e^{p_2 t}= \]

\[ =(U_{c_0}+U)R_1 C_1 \left[ \frac{e^{p_1 t}}{2R_1 C_1 R_2 C_2 P_1+R_1 C_1+R_1 C_2+R_2 C_1} +\right. \]

\[ \left. +\frac{e^{p_2 t}}{2R_1 C_1 R_2 C_2 P_2+R_1 C_1+R_1 C_2+R_2 C_1} \right], \]

substituting the values of \(P_1\) and \(P_2\), we obtain

\[ U_{R_1}(t)=(U_{c_0}+U)R_1 C_1 \left[ \frac{e^{p_1 t}-e^{p_2 t}} {\sqrt{(R_1 C_1+R_1 C_2+R_2 C_1)^2-4R_1 C_1 R_2 C_2}} \right]. \]

The voltage across the gap is

\[ U= \frac{U_{R_1}(t)} {R_1 C_1 \left( \frac{e^{p_1 t}-e^{p_2 t}} {\sqrt{(R_1 C_1+R_2 C_1+R_1 C_2)^2-4R_1 C_1 R_2 C_2}} \right)} -U_{c_0}. \tag{4} \]

For the adopted recording circuit

\[ R_1=510\cdot 10^3\ \text{ohm}, \qquad R_2=610\ \text{ohm}, \]

\[ C_1=5\cdot 10^{-12}\ \text{F}, \qquad C_2=4700\cdot 10^{-12}\ \text{F}, \]

\[ P_1=-0.7\cdot 10^3, \qquad P_2=-3.29\cdot 10^8, \]

then

\[ U=\frac{U_{R_1}(t)\,942}{e^{-0.7\cdot 10^3\cdot t}-e^{-3.29\cdot 10^8\cdot t}}-U_{c_0}. \]

The solution for the recording circuit with damping resistance has the same form as for the circuit without damping, with the exception of the term \(e^{-3.29\cdot 10^8\cdot t}\), which introduces an error at small times for the adopted recording circuit.

At \(t=1\cdot 10^{-6}\ \text{s}\)—the upper limit of the amplifier path of the C1-7 oscillograph—the error is

\[ \delta=\frac{1-e^{-0.7\cdot 10^3\cdot t}+e^{-3.29\cdot 10^8 t}}{1}\cdot 100=3.7\%. \]

At \(t=300\cdot 10^{-6}\ \text{s}\) (the longest times of the recorded processes)

\[ \delta=\frac{1-e^{-0.7\cdot 3\cdot 10^{-4}\cdot 10^3}+e^{-3.29\cdot 10^8\cdot 3\cdot 10^{-4}}}{1}\cdot 100=19\%. \]

Thus, the voltage across the spark gap can be determined from the obtained oscillogram and the known value of \(U_{c_0}\), with a known error determined by equation (4).

Calculation of Energy

The energy \(W\) released in the spark gap can be calculated from the voltage and current oscillograms (Fig. 5) by the formula

\[ W=\frac{S_u \cdot S_i \cdot m_u \cdot m_i \cdot m_t^2}{t}\ \text{J}. \]

Here \(S_u\) and \(S_i\) are the areas determined, respectively, from the voltage and current oscillograms; \(m_u\) and \(m_i\) are the scale, or tube sensitivity, respectively for voltage and current; \(m_t\) is the scale along the time axis; and \(t\) is the time determined from the oscillograms.

Fig. 5. Oscillogram of current (lower) and voltage during breakdown of a spark gap. Time marks at intervals of \(0.2\ \mu\text{sec}\).

To find the area \(S_u\), it is necessary to draw a “new” abscissa axis on the obtained voltage oscillogram, separated from the zero line of the oscillogram by the value \(U_{c_0}\), determined by the voltmeter or from the oscillogram immediately before breakdown, converted according to the scale \(m_u\) in mm, and to calculate the area under the damped sinusoidal voltage varying relative to the “new” abscissa axis.

Explosion Chamber

The explosion chamber (Fig. 6) serves for filling with the gas mixture under investigation; it is a glass bell jar, which is closed at the top by a vacuum plate (the latter has a valve switchable to three positions: for creating a vacuum in the chamber volume, filling it with the investigated gas mixture, and communicating with the atmosphere) and by a safety valve.

Electrode holders are introduced coaxially from the sides of the chamber; they have collet clamps for fastening electrodes of various diameters ranging from \(0.2\ \text{mm}\) to \(3\ \text{mm}\).

The electrical wires of the measuring circuit are connected directly to the collet clamps. One of the electrode holders is ex—

One of the rods is fixed, the other—grounded—is movable. Movement is carried out in the vertical and horizontal planes and along the axis of the electrode holders.

The optical device for measuring the distance between the electrodes consists of a monocular microscope with a folding bracket. When measuring distances, readings are taken from a limb and vernier.

Perpendicular to the plane of the electrodes, in the side wall of the chamber, there is a quartz-glass window for ultraviolet illumination of the gap between the electrodes.

The electrical characteristics of the explosion chamber are: capacitance of the connecting wires, 6 pF; capacitance of the electrodes with the chamber cover removed, 4 pF; capacitance of the electrodes with the chamber cover closed, 8.4 pF; capacitance of the electrodes with connecting wires, 14.4 pF.

Fig. 6. Photograph of the explosion chamber with electrode and optical devices.

The installation also includes the following units:

1. A temperature regulator, allowing the temperature in the explosion chamber to be regulated within the range 20–115°C with an accuracy of ±2°C.
2. A unit for storing the amplitude of the current flowing in the generating circuit, with measurement limits of (0.5–1000) A.
3. A peak voltmeter with limits for measuring the voltage on the generating capacitance of (0.5 ÷ 8) kV.
4. An electric charge carrier.
5. A block of generating capacitances, allowing the capacitance to be varied from 15 pF to 10 μF.
6. A high-frequency pulse generator with a repetition frequency of up to 1 kHz.

All units of the explosion-chamber installation are mounted in the form of a rack.

REFERENCES

1. L. R. Neiman, P. L. Kalantarov. Theoretical Foundations of Electrical Engineering, Part II, Gosenergoizdat, 1954.