A significant number of fire-induced power disruptions are observed in several countries every year. The faults are normally phase-to-phase short circuiting or conductor-to-ground discharges at mid-span region of the high-voltage transmission system. In any case, the wildfire plumes provide a conductive path. The electrical conductivity is due to intense heat in combustion zone of the fire which creates ion and electrons from flame inherent particulates. Increase in the ion concentration increases the electrical conductivity of the fire plume. The main purpose of this study was to measure dielectric breakdown electric field for vegetation and hydrocarbon flames. The experimental data is needed for validation of simulation schemes which are necessary for evaluation of power grid systems reliability under extreme wildfire weather conditions. In this study, hydrocarbon and vegetation fuels were ignited in a cylindrically shaped steel burner which was fitted with type-K thermocouples to measure flame temperature. The fuels consisted of dried weeping wattle ( Peltophorum africanum) litter, butane gas and candle wax. Two pinned copper electrodes supported by retort stands were mounted to the burner and energized to a high voltage. This generated a strong electric field sufficient to initiate dielectric breakdown in the flames. Breakdown electric field strength ( Ecrit) obtained from the experiment decreased from 10.5 to 6.9 kV/cm for the flames with temperature range of 1003 to 1410 K, respectively.
Over the last decade, Southern Africa has experienced significant socio-economic growth. To sustain the economic development in the region, there is necessity for reliability of electrical power supply. However, there has been an inadequate supply of the resource to sub-region and the demand for the resource is projected to be at 610,000 GWh by 2025 [
The faults are normally phase-to-phase short circuiting or conductor-to-ground discharges at mid-span region of the high-voltage transmission system. In any case, the wildfire plumes provide a conductive path [
Several researchers acknowledge that temperature and ionization are major factors that influence to the fire-induced flashover [
It is intended in the study to: 1) measure dielectric breakdown electric field for vegetation and hydrocarbon flames at atmospheric pressure; the experimental data is needed for validation of simulation schemes which are necessary for evaluation of power grid systems reliability under extreme wildfire weather conditions; 2) simulate the parameter for flame at normal temperature gradient. Even though the parameter has been measured for other types of flames, there are a lot of inconsistencies in values obtained from the experiments, e.g., in [
Electro-thermal properties of a gas dynamic boundary layer between electrodes and combustion plasma are critical in conduction of electric current through the plasma. Increasing the applied potential on the electrode decreases the depth of the electrostatic sheath around the electrode, thereby increasing the probability of conduction through the plasma. Section 2 discusses relevant theory on the initiation of an electrical discharge from an energized electrode through the plasma. In the Section, the relation between critical breakdown electric field strength and electrode-plasma temperature gradient is derived from energy balance relation in the boundary layer adjacent to the electrode surface. It is then simulated for normal flame temperatures. A discussion on the experimental method to measure critical breakdown electric field strength is given in Section 3 of the manuscript. The results from the experiment are given and discussed in Sections 4. Conclusions and future research direction are given in the last Section of the manuscript.
Consider two pin electrodes, separated by a distance “d”, inserted in a weakly-ionized combustion plasma in thermal equilibrium (
∂ T ∂ t + ( v g ∇ ) T = λ T ρ g C p ∇ 2 T + σ ρ g C p E 2 (1)
where: T, ρg, Cp, E, λT and σ are plasma temperature, gas density, specific heat capacity, electric field strength, thermal and electric conductivity.
Under steady state conditions and noting that plasma gas flow is transverse to the direction of electric discharge (
λ T ∇ 2 T = σ E 2 (2)
Integrating Equation (2) over electrode gap distance and across temperature gradient, (i.e., from; x = 0 to d and Ts to Tf) gives the following relation (Messerle et al. [
Λ ( 1 − β ) = x d ( 1 − β ) (3)
where Λ = 2 λ T σ E 2 ( T f − T s ) and β = x d .
At breakdown, d becomes small as the plasma sheath depth is reduced and consequently β becomes large. Rearranging Equation (3) and simplifying gives:
Λ = d 2 (4)
where; x = d .
Following from (3) and (4), the critical electric field strength at breakdown is given by the expression:
E c r i t = 1 d 2 λ T σ ( T f − T s ) (5)
Simulation for the Ecrit was done to determine its expected range under normal flame conditions. A potassium-seeded hydrocarbon flame of the following temperature-dependent electro-physical properties was considered:
a) Electron density (Ne):
The electron density in the flame was determined by using Saha equation for thermal ionization shown below as:
N e = ( K 1 N p ) 1 / 2 [ ( 1 + K 1 4 N p ) 1 / 2 − ( K 1 4 N p ) 1 / 2 ] cm − 3 (6)
where K1 and Np are as calculated in Mphale et al. [
b) Thermal conductivity:
Analytical expression for the thermal conductivity was derived from a linear fit of experimental data from Chandra et al. [
λ T = 3.86 × 10 − 5 T + 0.08 W ⋅ m − 1 ⋅ K − 1 (7)
Pearson correlation coefficient (r) for fit was 0.97.
c) Sheath depth:
Chandra et al. [
d = − 1.91 × 10 − 7 T + 2.92 × 10 − 4 m (8)
The Pearson correlation coefficient (r) for fit was 0.98.
Electrical conductivity of the combustion plasma to be determined from the relation [
σ = N e q 2 m e φ e f f s − 1 (9)
where φ e f f is electron momentum transfer collision frequency. It is approximated to be 1 × 1012 s−1, e.g. in Letsholathebe and Mphale. [
The critical electric field strength was simulated using Equation (5) for the normal combustion flame temperature. The simulated field strength is shown in
Biomass and hydrocarbon fuels were ignited in a cylindrically shaped steel burner (
the flames. The potential difference between the electrodes was increased at a steady rate of 0.2 kV per 10 seconds until breakdown occurred. As the applied potential difference was increased, it was monitored through an oscilloscope. A sensitive multimeter (UNI-T UT 803) was used to measure current through the circuit during the experiment (
The biomass sample used in the experiment consisted of litter fall from Peltophorum africanum tree sampled randomly from an open woodland habitat in Mogoditshane (Kweneng District, Botswana). The tree is endemic to most parts of Southern Africa, mainly in wooded grasslands. It is known to contain reasonable amounts of macronutrient which includes; phosphorus, calcium, magnesium, sodium and potassium (Mongalo [
The litter fall was dried in the laboratory for about 5 days before it was burnt so as to improve combustion efficiency. Combustion of the plant matter is a complex process that depends on the amount of oxygen available and prevalent weather conditions. Jenkins et al. [
C x 1 H x 2 O x 3 N x 4 S x 5 Cl x 6 Si x 7 K x 8 Ca x 9 Mg x 10 Na x 11 P x 12 Fe x 13 Al x 14 Ti x 15 + n 1 H 2 O + n 2 ( 1 + e ) ( O 2 + 3.7 6N 2 ) ⇒ n 3 CO 2 + n 4 H 2 O + n 5 O 2 + n 6 N 2 + n 3 CO 2 + n 4 H 2 O + n 5 O 2 + n 6 N 2 + n 12 HCl + n 13 KCl + n 14 K 2 SO 4 + n 15 C + ⋯ (10)
The first reactant in Equation (10) is an incomplete empirical formula for plant material [
Butane is a naturally occurring gaseous alkane which is produced from fractional distillation of crude oil. The chemical formula of the gas is C4H10. The fuel exists in two structural isomeric forms; normal butane (n-butane) and iso-butane. The two isomers have a slightly different combustion characteristics and reaction rate when placed under similar combustion conditions (Wilk et al. [
In the experiment, pressurized n-butane contained in 190 g cartridge was used for its quiet, clean and controllable flame. When ignited in air adiabatic temperature of butane flame could reach about 1970˚C (Ševčik et al. [
2 C 4 H 1 0 + 1 3 O 2 ⇒ 8 C O 2 + 1 0 H 2 O (11)
A candle is an ignitable wick embedded in paraffin wax. The wax is a mixture of saturated straight-chained solid alkanes (i.e., hydrocarbons with a general formula given by C n H 2 n + 2 ). For a candle paraffin wax, n ranges from 19 to 36 with an average value of 25. The wick is often made from braided or twisted cotton fabric. On average, heat of combustion for a candle is 43.1 MJ/kg and it has been observed that the fuel is the safest sources of light and heat energy. A candle flame is of diffusion laminar type with temperature with temperature ranging from 600 to 1400˚C (Gaydon and Wolfhard, [
C 2 5 H 5 2 + 0 . 3 1 C 1 8 H 3 6 O 2 + 4 6 . 0 6 ( O 2 + 3 . 7 6 N 2 ) ⇒ 3 0 . 5 8 C O 2 + 3 1 . 5 8 H 2 O + 1 7 3 . 1 9 N 2 (12)
There are different types of candles depending on the purpose for which they are used, e.g. tapper, votire. In the experiment, a tapper white wax Prices Lighthouse® candle of diameter 2.0 cm and height 25.0 cm was used. The combustion rate of the candles is estimated at 0.11 g/min (Hammins and Bundey, [
A thermocouple “tree” of about 20.0 cm high was constructed from steel rods of 2.0 cm diameter. A rectangular base (10.0 × 15.0 cm) was wielded to the tree “stem” for it to stand firmly upright. Two side “arms” of length 10.0 cm were attached at positions; 10.0 and 14.0 cm from the tree base to hold two thermocouples. Thermocouples used were made from insulated chromel-alumel thermocouple wire 50 μm in diameter. The thermocouple wire had shield which can withstand high temperatures. The type K thermocouple wires were then electrofused at one end to make perfect junction (bead). The thermocouples were calibrated using a hot air gun and a multimeter. They were then fixed to the tree “arms” by means of a muffler tape and the junctions were left protruded 1 cm beyond the “arm” length into the flame. The thermocouples were then wired to Campbell Scientific CR1000® data logger to read in the temperatures in to a computer throughout each experiment.
Two copper electrodes of diameter 0.80 cm were sharpened to hemispherical tips of diameter 0.06 cm and used to generate an intensified electric field within the fuel flames. They were mounted to the steel cylindrical burner through 1.20 cm diametrically oppose holes. This allowed the distance between them to be varied. The electrodes were held in position by insulated retort stand clamps. A positive terminal of a PHYWE® high voltage dc power supply was connected to one electrode while its negative terminal was connected to the other. The power supply had the capacity to produce 10 kV potential difference. The power supply had a current surge protector. A circuit diagram which shows experimental set up is shown in
Flames up to 20 cm high were observed during the combustion of Peltophorum africanum litter as air entrained through the holes of the cylindrical burner to facilitate near-efficient combustion. The flames from the combustion of litter took 60 - 80 seconds to extinguish while flame from other fuels persisted for more than 250 seconds. It took 40 seconds for Peltophorum africanum flames to fill the space inside the burner. The flame reached its maximum temperature of 1022 K after 50 seconds. Temperatures measured at the fuel-flame interface during combustion of the three fuels are shown in
It was observed from
As for the candle flame, its temperature was observed to rise rapidly to reach a maximum of 988 K in 45 s. It then decreased steadily to a minimum of 656 K at 75 seconds after ignition as the flame was deflected away from the thermocouple bead. It was noted that there was no wind that initiated the flame deflection. This occurred just before dielectric breakdown. Thereafter, the flame temperature rose to a maximum of 914 K at 100 seconds after ignition and continued to burn at an average of 771 K until the candle flame was extinguished.
It took longer for Peltophorum africanum flame to reach its maximum temperature compared to the other fuels as flaming depended on the time taken for volatilization of flammable pyrolysates to occur. The vegetative material has to thermally decompose first for ignition to occur.
At about 65 seconds after the butane fuel was ignited, high voltage dc was applied to one the pinned electrodes at a steady rate 0.02 kV per second. This generated electric field strength between the electrodes which was amplified due to the hemispheric shape of the electrode tip. The electric field produced by the pinned electrodes (Epp) is given by the expression:
E p p = V p ln { ( 1 + η 0 ) ( 1 − η 0 ) } ( a ( a 2 − x 2 ) ) (13)
where
η 0 = ( d / 2 ( d / 2 ) + R ) 1 / 2
a = ( ( d / 2 ) ( ( d / 2 ) + R ) ) 1 / 2
R = radius of curvature for the tip;
d = inter electrode gap.
It was observed that the potential difference was rising at the steady rate up to 140 seconds after ignition. This was the times at which breakdown occurred. The breakdown voltage (Vcrit) was determined from potential difference across R2 (
V c r i t = { ( R 1 / R 2 ) × V 2 c r i t } (14)
where: R1 = 108.2 MΩ;
R2 = 9.7 kΩ;
V2crit = potential difference across R2 at breakdown.
As it is shown in
At about 10 seconds from the ignition time, high voltage dc was applied to pin copper electrodes separated by a distance of 0.14 cm. When the potential difference was applied at the rate of 0.3 kV per second after 10 seconds, it took 65 seconds for breakdown to occur (
The voltage across R2 decreased at a steeper rate until it reached value of 354 mV after 85 seconds since ignition. After 90 seconds, there was a decrease of potential difference across R2 at an average rate of 5.5 mV/s until after 115 seconds. A very small potential difference was recorded soon after 120 seconds.
When a high voltage dc potential difference was applied to pin copper electrodes
separated by a distance of 0.06 cm in vegetation litter flame at a constant rate of 0.2 kV per 10 seconds, a breakdown voltage of 1.120 kV was obtained (
After the breakdown voltage, the potential difference across R2 decreased at a steeper rate until it reached value of 15 mV after 90 seconds after ignition. There was a steady small decrease in potential difference across R2 between 80 and 100 seconds. A small jump in the potential was observed thereafter.
From the above observations, breakdown electric field strength for the flames were calculated using distances between electrodes. It was observed that separation distances between electrodes were: 0.06, 0.14 and 0.22 cm for vegetation litter, candle and butane flames, respectively. The calculated breakdown electric fields are shown in
The measurement of dielectric breakdown for the vegetation and hydrocarbon
flames has been performed using the pin electrodes. The pin electron enhanced the electric field in the flame gap so much that the conduction occurred at lower potential differences compared to other procedures e.g., using parallel plates. The maximum potential difference applied between the electrodes was 2.2 kV. The dielectric breakdown electric field strength for the flames ranged from 6.9 to 10.5 kV/cm for maximum temperatures of 1400 to 1003 K, respectively. Of the flames considered, vegetation flame had the highest dielectric breakdown electric strength even though its maximum temperature was slightly higher than that of candle flame. This was because of the effect of soot which has bridged the spark gap.
Maabong, K.E., Mphale, K., Letsholathebe, D. and Chimidza, S. (2018) Measurement of Breakdown Electric Field Strength for Vegetation and Hydrocarbon Flames. Journal of Electromagnetic Analysis and Applications, 10, 53-66. https://doi.org/10.4236/jemaa.2018.103004