The effect of air pressure on evolution of gas density

The effect of air pressure on evolution of gas density and temperature inside a leader channel Xinyu Ma1, Chijie Zhuang1, Zezhong Wang1, Yingzhe Cui1, Rong Zeng1,* 1Department of Electrical Engineering, State Key Lab of Power System Tsinghua University Beijing, China [email protected] Abstract—The discharge processes in a 40-cm rod-plate air gap were experimentally studied under different air pressures. Mach-Zehnder interferometry was used to analyze the gas density and temperature evolution in the discharge channel, and the effect of air pressure on the evolution of gas density and temperature in the leader channel was obtained. When the reduced electric field E/N is constant, the decrement of the gas density and the maximum temperature in the leader temperature decreases as the pressure increases.

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Te Li2 State Grid Zhejiang Electric Power Research Institute Zhejiang, China

The internal structure of the climate chamber is shown in Fig. 1.

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Keywords—leader channel, air pressure, gas density, gas temperature, Mach-Zehnder interferometry

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I. INTRODUCTION Leader discharge is an important mechanism for breakdown in long air gaps, including cloud-to-ground lightning. The peculiarities of leader at different air pressures are of great interest. As altitude increases, the atmospheric pressure decreases. The situation with a tropospheric lightning is formed at pressures of the order of 100 Torr or less which is quite different from that at atmospheric pressure. In addition, with the continuous development of UHV technology, the voltage level of transmission lines is continuously increasing. However, the high-altitude areas where the UHV transmission line is located have a lower atmospheric pressure, which puts forward higher requirements on the insulation[1]. The temperature in the discharge channel directly affects the ionization mechanism in discharge process, and is one of the most important characteristics of differentiating leader discharge and streamer discharge. According to the ideal gas equation, the rise of the gas temperature in the leader channel directly corresponds to the decrease of the relative gas density. In this paper, the discharge processes in a 40 cm rod-plate air gap were experimentally studied under different air pressures. A brief description of the experimental techniques was introduced in section II, and the analysis method was discussed in section III; the leader inception criterion was discussed in section IV. Finally, typical experimental results were given in section V. II.

EXPERIMENTAL SET-UP

A. Climate Chamber To study the effect of air pressures on gas density and temperature evolution of a leader channel, a closed artificial climate chamber was constructed. It can control the environment variables in long air gap discharge experiments. This work is supported by the national science of China under project 51577098. 978-1-5386-6635-7/18/$31.00 ©2018 IEEE

12 4 13 14 16 17

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5 15

11 10 6 7

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Fig. 1. Internal structure of the climate chamber.

When adjusting the air pressure in the chamber, the relative air humidity will increase or decrease sharply as the pressure increases or decreases without any intervention. If the relative humidity of the air is about 50% at atmospheric pressure, the relative humidity will approach 100% when the pressure increases to 2 atm. It is to say, the atmospheric pressure and the relative humidity change simultaneously and are hard to be decoupled. To decouple ambient humidity and air pressure, the air, which enters the climate chamber, must be absolutely dry. There are two solutions. One is adding strict filtering processes in the air intake of the climate chamber and the other is ensuring the air source is absolutely dry. The results of the two solutions are shown in Fig. 2

B. Time-resolved Mach-Zehnder Laser Interferometry The temperature and density inside the discharge channel are important characteristics of discharge process. It is widely accepted that the temperature in the leader channel can be up to 1500 K, while in the streamer channel it is close to the ambient temperature. Different temperature ranges will directly affect the ionization mechanism in discharge process, which differentiates leader discharge and streamer discharge. So obtaining temperature evolution law in discharge process is very important.

Fig. 2. Results of solutions to decouple air density and humidity (red dots represent the relative humidity after adding two levels of filtering; blue dots represent the relative humidity when using dry synthetic air at the air source).

It shows that after adding these solutions, air pressure and humidity can be decoupled obviously. However, because the chamber is large, the former solution’s decoupling result is worse than that of the latter. But the air source of the former is compressed air, which can be obtained easily and locally. Synthetic air is a mixture of high purity gas, so the latter solution is limited by the volume and the number of gas cylinders. Thus, we combined the two solutions together to change the air pressure in climate chamber. When the experimental pressure condition was lower than 1.5 atm, synthetic air was used. And when it was higher than 1.5 atm, compressed air with filter processes was used. The artificial climate chamber includes a chamber body (1), a wall bushing (2), an air-drying device outside the chamber body (connected to valve 15), an atomizer (connected to 15 through the air-drying device), and a temperature and humidity measuring instrument (connected to interface 5). Absolute dry synthetic air can be injected from valve 13, on which an air outlet 14 is set. The mark numbers 6~10 are mechanical components which are used to change the gap distance (vertical distance between 4 and 11). The gap distance of the chamber can be adjusted from 5 to 70 cm. Moreover, Observation windows (3), two light-transmitting lens (4), positive and negative barometers (16, 17) are respectively installed on the lateral wall of the chamber body. The precision of air pressure is 0.05 bar for the pressure below 1 bar and 0.25 bar at 1~8 bar because of the scales of positive and negative barometers. The mark number 12 is a

Gas refractive index is closely related with gas density and the gas temperature can then be obtained by using ideal gas equation. Mach-Zehnder interferometry was chosen to observe the change of gas refractive index[12]. The sketch map of M-Z interferometer is shown in Fig. 3.

Fig. 3. Beam path diagram of M-Z interferometer.

In Fig. 3, BS1 and BS2 are two beam splitters. M1 and M2 are two reflector mirrors. The length of the optical path (the distance between M2 and BS2) was set to approximately 2 m. 2 m is enough to ensure the requirement of insulation since the discharge is triggered in the chamber. C. Characteristics of Air Gap Discharge Platform The applied voltage waveform on the air gap was positive IEC standard switching impulse (250/2500 μs). In the work, the reduced electric field was kept constant and the amplitude of applied voltage increased with the atmospheric pressure. The voltage amplitude and environmental parameters in the experiments are shown in Tab. I. TABLE I. VOLTAGE AMPLITUDE AND ENVIRONMENTAL PARAMETERS IN THE TEST

relief valve in case that the chamber bursts because of high pressure. The wall bushing extends vertically into the lower end of the inside of the chamber and it is installed with a discharge electrode on the high voltage side. Its upper end protrudes from the chamber body and is connected with the high voltage leading wire to apply high voltage to the air gap. The wall bushing is the high voltage side, and the chamber body and the plane electrode are low voltage sides for security. The chamber has the characteristics of high pressure and voltage resistance, and an easily adjustable gap size with a wide range.

In this work, a 40 cm rod-plate air gap with a 1.5 mm uniform rod electrode radius was used and the air gap was broken down. For the voltage generation and measurement system, the voltage source used in the experiment was a 1200 kV / 60 kJ impulse voltage generator. The discharge current was

measured by a 0.5 Ω coaxial shunt and its measuring results were compared with a Rogowski Coil. Two high speed CMOS cameras were used for the discharge morphology observation. Camera 1 was used to observe laser spot produced by the laser generator in MechZehnder interferometry, and camera 2 was used to observe the discharge channel lighting morphology. To synchronize the two high speed cameras and the current measuring system, DG535 was used to trigger the devices. III.

ANALYTICAL METHOD

A typical set of interference fringes is shown in Fig. 4. The air pressure in the climate chamber was evacuated to 0.4 atm by a negative pressure pump. Frame (a) is the base interference fringe without discharge distortions. Camera 1 has a significant but unknown trigger delay. Through the current and voltage waveforms, the real breakdown time of a discharge can be confirmed. Camera 1 can also get a breakdown time. The difference between the two breakdown time is the trigger delay time. By comparing the results of many times of experiments, the trigger delay time was recognized as 28 μs. Thus, the frames in Fig. 4 (b ~ e) correspond to the real discharge moment after applying voltage are 142.43 μs, 146.50 μs, 150.57 μs, 154.64 μs.

n( r ) = n0 −

λ ∞ dδ ( x) / dx ⋅ cos β dx π r x 2 − r 2

(1)

where n0 is air refractive index under the conditions of initial changed pressures and 273 K. β is the projection tilt angle of the leader channel in the orthogonal observation direction of the interference. That is, due to the discharge channel's inclination, the area through which the light beam passes is actually an ellipse and therefore it needs to be corrected. An example of the luminescent images shot by camera 2 are shown in Fig. 6. The leader channel on the right was the one that broke through the air gap. The angle β is shown in Fig. 6 (b), which is 36°.

Fig. 5. Axisymmetric field cross section of the leader channel for Abel inverse transformation.

β

(a)

(b)

(c)

(d)

(a)

(b)

Fig. 6. Luminescent images of discharge channels shot by camera 2.

(e) Fig. 4. A typical set of interference fringes at 0.4 atm, where (a) is the base interference fringe without discharge distortions and (b~e) correspond to the real discharge moment after applying voltage 142.43 μs, 146.50 μs, 150.57 μs, 154.64 μs.

The leader channel can be approximated as a segmented cylinder. The parameter distribution is axisymmetric, i.e., any cross section of a leader channel is perpendicular to the axis of the leader channel and the leader channel parameters are assumed to be functions of only the radial position r. Fig. 5 shows a schematic diagram of the cross-section of a light passing through a cylindrical axis. The Abel inverse transformation transforms the distribution of the fringe displacement δ in the x direction into the distribution of the refractive index in the radial direction r in the leader channel,

Abel inverse transformation of the fringe displacement δ derives the refractive index of air. The electronic and neutral particles dominate the refractive index. Due to the low degree ionization of the leader discharge, the order of electron density (1014 cm-3) is much smaller than that of neutral particles density (1019 cm-3). Thus, the contribution of electrons to refractive index is much smaller than that of neutrals. The refractive index difference n-1 (the difference between the refractive index n of the gas and refractive index of the vacuum 1) of the gas is proportional to the gas density under the assumption that the neutral particle components remain unchanged, as indicated in (2).

ρ ( r ) n( r ) − 1 = n0 − 1 ρ0

(2)

Except for drastic changes in gas status during the streamer-to-leader transition, the pressure of the gas in the channel can be approximated as a constant during the

Th (r ) = IV.

Using the analytical methods above, the corresponding one-dimensional distribution of gas density and temperature under the four conditions 0.4 atm, 1 atm, 1.5 atm, 2 atm are shown in Figs. 7-10. 1.2

142.43μs 146.50μs 150.57μs 154.64μs

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Gas Temperature（ K）

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Fig. 7. The evolution of gas temperature and gas density one-dimensional radial distribution inside leader channel at 0.4 atm. t=94.70μs t=98.77μs t=119.12μs t=127.26μs t=131.33μs

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Fig. 8. The evolution of gas temperature and gas density one-dimensional radial distribution inside leader channel at 1 atm. 1400


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t=12.22μs t=28.82μs t=32.14μs t=35.46μs

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Fig. 9. The evolution of gas temperature and gas density one-dimensional radial distribution inside leader channel at 1.5 atm.

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Fig. 10. The evolution of gas temperature and gas density one-dimensional radial distribution inside leader channel at 2 atm.

The zero-time interval in Figs. 7-10 is the time interval that voltage was applied on the air gap. The last moment in each figure is the moment of the final photo shot before breakdown. According to Figs. 7-10, when reduced electric field is constant, as the external gas pressure increases, the decrement of gas density and temperature in the leader channel during the whole development process will decrease. Particularly, the gas temperature of the leader channel center shows an obvious downward trend. Quantitatively, the gas temperature reduced from up to 3700 K to 950 K and the decrement in gas density decreased from a maximum of 0.92 bar to a maximum of 0.71 bar as the pressure increased from 0.4 atm to 2 atm. V.

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Discharge was carried out at 0.4 atm, 1 atm, 1.5 atm, 2 atm. Since the leader channel is approximated as a segmented cylinder, parameters are assumed to be functions of only the radial position r. So the evolution of gas density and temperature in the leader channels were quantitatively analyzed from the beginning and developing to prebreakdown processes in a one-dimensional distribution.

3500

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(3)

EXPERIMENTAL RESULTS

4000

t=12.22μs t=28.82μs t=32.14μs t=35.46μs

900


ρ0 ⋅T ρ (r ) 0

1000


development and expansion of the leader channel[3], and the gas approximately satisfies the ideal gas equation of state where gas density and temperature are inversely proportional. Thus, the radial distribution Th (r ) of the gas temperature in the leader channel can be further determined by (3).

DISCUSSION

It may be concluded from this paper that the gas temperature in the leader channel will decrease as the air pressure increases. It is widely accepted that the temperature in the leader channel can be up to 1500 K[45]. However, the criterion was obtained at atmospheric pressure. The discharge current image at 2 atm is shown in Fig. 11 (after subtracting the capacitive current). The discharge corresponds to the gas density and temperature evolution in Fig. 10. It can be seen that there was a large current pulse of amplitude 2 A around 45.8 μs, and then the current was continuous, which indicated the leader inception[6]. At 63 μs the current increased drastically and the gap was broken down. Bazelyan concluded that the streamer-to-leader transition time τ for 0.3 atm is much slower than for 1 atm. And for a leader channel propagating in air with a typical velocity of 1 – 3 cm/μs, the duration of the heating process from 300 K to 1500 K is no longer than 0.3 μs[78]. Based on this regulation, the transition time for 2 atm should be shorter. Popov did simulation to obtain that the discharge channel temperature rose up to 1500 K on time scales of 90 – 100 ns at atmospheric pressure[9]. In our experiments, the time from the inception of leader to the breakdown of this discharge was much longer than the acknowledged transition time τ. Thus from this perspective, the discharge had produced a leader channel.

channel center temperature did not exceed 1000 K, which is reasonable. However, the leader inception criterion needs further research and discussion. VI.

Fig. 11. Discharge current at 2 atm.

Considering the trigger delay time of camera 1, the corresponding interferometry image of the time 45.8 μs is shown in Fig. 12. The leader channel on the left was the one that broke through the gap. The fringe displacement δ had been obvious enough. In addition, the velocity of the discharge channel can be obtained from luminescent images. It is of 1 cm/μs magnitude, which is the typical velocity of leader channel[10].

Fig. 12. Corresponding interferometric fringe image at 2 atm.

In conclusion, from the current image and interferometry image, the discharge channel had completed the streamer-toleader transition and produced a leader channel before breakdown. At atmospheric pressure, at the beginning of streamerto-leader transition, electron impact ionization and electron attachment maintain the basic stability of the electron density. As the gas temperature increases, electron detachment reactions and thermal associative ionization reactions become the main ways of generating electrons. Thus, it is necessary to heat the cold air in the streamer channels to temperatures T ≥1500–2000 K in order for streamer-to-leader transition to occur. When the air pressure reaches 2 atm high, with a lower reduced electric field, electron impact ionization rate becomes slower. The conductivity in the channel and the inject energy decrease. These lead to a lower temperature. Thus, the rate of thermal associative ionization is lower than that at atmospheric pressure. This will again lead to a less increment of electron density. For this cycle, the achievable maximum gas temperature at 2 atm is absolutely lower than that at 1 atm. In our experiment, the maximum discharge

CONCLUSION

The atmospheric pressure in the artificial climate chamber was changed from 0.4 atm, 1 atm, 1.5 atm to 2 atm through the decoupling adjustment of the atmospheric pressure and humidity. The Mach-Zehnder interferometry was used to analyze the evolution of gas temperature and gas density in leader channels quantitatively. It is concluded that when the reduced electric field E/N is constant, the decrement of the gas density and the maximum temperature in the leader channel will decrease as the pressure increases. When the pressure increases from 0.4 atm to 2 atm, the gas temperature in the leader channel center reduced from up to 3700 K to 950 K and the decrement in gas density at the center also decreased from a maximum of 0.92 bar to 0.71 bar. ACKNOWLEDGMENT This work was supported by the national science of China under project 51577098. REFERENCE [1]

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