Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites
This work is devoted to investigation of the radiation in the plasma of electric arc discharge between Cu-C composite electrodes and estimation of its contribution during the determination of electron density from the energy balance equation (Elenbaas-Heller). The contribution of radiation energy in...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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Veklich, A. Fesenko, S. Murmantsev, A. Boretskij, V. 2023-12-05T10:06:45Z 2023-12-05T10:06:45Z 2021 Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites / A. Veklich, S. Fesenko, A. Murmantsev, V. Boretskij // Problems of Atomic Science and Technology. — 2021. — № 4. — С. 157-161. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 52.70.-m https://nasplib.isofts.kiev.ua/handle/123456789/195422 DOI: https://doi.org/10.46813/2021-134-157 This work is devoted to investigation of the radiation in the plasma of electric arc discharge between Cu-C composite electrodes and estimation of its contribution during the determination of electron density from the energy balance equation (Elenbaas-Heller). The contribution of radiation energy in heat transfer is estimated as well. The calculation is carried out based on the preliminary experimentally obtained radial distribution of plasma temperature. For the correct solution of the energy balance equation, a Gaussian approximation of the plasma temperature profile is used. Estimation of the total current was used as a criterion for the need to take into account the radiation in the diagnostics of electric arc plasma. Робота присвячена дослідженню випромінювання в плазмі дугового розряду між композитними Cu-C електродами та оцінці його внеску при визначенні електронної концентрації з рівняння енергетичного балансу (Еленбааса-Геллера). Також оцінюється внесок енергії випромінювання в процеси теплообміну. Розрахунок проводиться на основі попередньо експериментально отриманого радіального розподілу температури плазми. Для коректного розв’язання рівняння енергетичного балансу використовується апроксимація профілю температури плазми функцією Гаусса. Оцінка загального струму використовується як критерій необхідності врахування випромінювання в діагностиці плазми електричної дуги. Работа посвящена исследованию излучения в плазме электродугового разряда между композитными CuC-электродами, а также оценке его вклада при определении электронной концентрации из уравнения энергетического баланса (Эленбаaса-Геллера). Также оценивается вклад энергии излучения в процессы теплообмена. Расчет проводится на основе предварительно экспериментально полученного радиального распределения температуры плазмы. Для корректного решения уравнения баланса энергии используется аппроксимация профиля температуры плазмы функцией Гаусса. Оценка полного тока используется в качестве критерия необходимости учета излучения в диагностике плазмы электрической дуги. This work has been carried out within the framework of the EURO fusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. In addition, authors are grateful to the partial support of these studies in the frame of project 19БФ052-02 of MES of Ukraine: “Investigation of properties of lowtemperature gas-discharge plasma for technological applications”. The authors also express their gratitude to Ministry of Education and Science of Ukraine for the support of project 21БП052-01 “Applications of electric discharge plasma with condensed dispersed phase”. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Gas discharge, plasma-beam discharge, and their applications Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites Оцінка ролі випромінювання в плазмі електродугового розряду між композитами Cu-C Оценка роли излучения в плазме электродугового разряда между композитами Cu-C Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites |
| spellingShingle |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites Veklich, A. Fesenko, S. Murmantsev, A. Boretskij, V. Gas discharge, plasma-beam discharge, and their applications |
| title_short |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites |
| title_full |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites |
| title_fullStr |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites |
| title_full_unstemmed |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites |
| title_sort |
estimation of the role of radiation in the plasma of electric arc discharge between cu-c composites |
| author |
Veklich, A. Fesenko, S. Murmantsev, A. Boretskij, V. |
| author_facet |
Veklich, A. Fesenko, S. Murmantsev, A. Boretskij, V. |
| topic |
Gas discharge, plasma-beam discharge, and their applications |
| topic_facet |
Gas discharge, plasma-beam discharge, and their applications |
| publishDate |
2021 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Оцінка ролі випромінювання в плазмі електродугового розряду між композитами Cu-C Оценка роли излучения в плазме электродугового разряда между композитами Cu-C |
| description |
This work is devoted to investigation of the radiation in the plasma of electric arc discharge between Cu-C composite electrodes and estimation of its contribution during the determination of electron density from the energy balance equation (Elenbaas-Heller). The contribution of radiation energy in heat transfer is estimated as well. The calculation is carried out based on the preliminary experimentally obtained radial distribution of plasma temperature. For the correct solution of the energy balance equation, a Gaussian approximation of the plasma temperature profile is used. Estimation of the total current was used as a criterion for the need to take into account the radiation in the diagnostics of electric arc plasma.
Робота присвячена дослідженню випромінювання в плазмі дугового розряду між композитними Cu-C електродами та оцінці його внеску при визначенні електронної концентрації з рівняння енергетичного балансу (Еленбааса-Геллера). Також оцінюється внесок енергії випромінювання в процеси теплообміну. Розрахунок проводиться на основі попередньо експериментально отриманого радіального розподілу температури плазми. Для коректного розв’язання рівняння енергетичного балансу використовується апроксимація профілю температури плазми функцією Гаусса. Оцінка загального струму використовується як критерій необхідності врахування випромінювання в діагностиці плазми електричної дуги.
Работа посвящена исследованию излучения в плазме электродугового разряда между композитными CuC-электродами, а также оценке его вклада при определении электронной концентрации из уравнения энергетического баланса (Эленбаaса-Геллера). Также оценивается вклад энергии излучения в процессы теплообмена. Расчет проводится на основе предварительно экспериментально полученного радиального распределения температуры плазмы. Для корректного решения уравнения баланса энергии используется аппроксимация профиля температуры плазмы функцией Гаусса. Оценка полного тока используется в качестве критерия необходимости учета излучения в диагностике плазмы электрической дуги.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195422 |
| citation_txt |
Estimation of the role of radiation in the plasma of electric arc discharge between Cu-C composites / A. Veklich, S. Fesenko, A. Murmantsev, V. Boretskij // Problems of Atomic Science and Technology. — 2021. — № 4. — С. 157-161. — Бібліогр.: 17 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2021. № 4(134) 157
https://doi.org/10.46813/2021-134-157
ESTIMATION OF THE ROLE OF RADIATION IN THE PLASMA
OF ELECTRIC ARC DISCHARGE BETWEEN Cu-C COMPOSITES
A. Veklich, S. Fesenko, A. Murmantsev, V. Boretskij
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
E-mail: murmantsev.aleksandr@gmail.com
This work is devoted to investigation of the radiation in the plasma of electric arc discharge between Cu-C com-
posite electrodes and estimation of its contribution during the determination of electron density from the energy
balance equation (Elenbaas-Heller). The contribution of radiation energy in heat transfer is estimated as well. The
calculation is carried out based on the preliminary experimentally obtained radial distribution of plasma tempera-
ture. For the correct solution of the energy balance equation, a Gaussian approximation of the plasma temperature
profile is used. Estimation of the total current was used as a criterion for the need to take into account the radiation
in the diagnostics of electric arc plasma.
PACS: 52.70.-m
INTRODUCTION
The development of sliding contacts for energy
transfer to a moving consumer is an important area of
power industry and electrical engineering [1]. Copper
and its alloys, in particular with aluminium, low-carbon
or graphitized steel, powder materials based on iron,
carbon and metal-carbon etc., are often used as materi-
als of sliding contacts. Moreover, there is still no single
solution to the problem of choosing the optimal compo-
sition of contacts.
First of all, it is necessary that the material used for
these elements provides reliable current collection, does
not undergo intense wear, be affordable and inexpen-
sive.
It is difficult to meet such requirements due to the
fact that the material of current-collecting elements
must have a number of incompatible properties, namely:
good mechanical and antifriction properties, low resis-
tivity and transient electrical resistance, high resistance
to electrical erosion. In addition, it is necessary that the
material of the current collector element guarantees
reliable operation of the high-current sliding contact in
difficult climatic conditions: with significant fluctua-
tions in temperature, humidity and contact failure [2].
Under such extreme operating conditions, there is sig-
nificant electrical erosion of the contact pair, due to the
high temperature and the occurrence of breaking electric
arcs.
Most often, sliding contacts are based on graphite,
which has excellent lubricating properties, high heat
resistance and low cost. The only disadvantage of
graphite is its relatively high electrical resistance, which
can be reduced with copper-graphite composites.
The above-mentioned electric discharge between
sliding contacts leads to their intensive wear, so it is
important to study such electrical erosion processes,
which were partially performed by the authors of [3 - 5],
who studied the effect of DC and AC arc discharge on
the electrode surface. Unfortunately, in these investiga-
tions the spatial resolution was not provided. Moreover,
there are no works that would be devoted to estimating
the effect of radiation during the diagnostics of such
type of plasma.
Thus, the main aim of this work is to estimate the
role of the radiation in the plasma of electric arc dis-
charge between composite Cu-C electrodes, as well as
to provide the diagnostic of such plasma with spatial
resolution.
1. ELENBAAS-HELLER EQUATION
In the case of axial symmetry of the arc discharge,
the energy balance equation (Elenbaas-Heller) is con-
venient to write in a cylindrical coordinate system [6]:
2 1 ,
dT rdr E r r r
r dr dr
(1)
where σ(r), λ(r), T(r), ρ(r) are the radial distributions of
electrical conductivity, thermal conductivity, tempera-
ture and density of radiation energy, respectively. E is
electric field strength of the positive column (directed
along the Z axis of the cylindrical coordinate system). It
should be noted, that equation (1) does not take into
account the convective cooling of the arc discharge, the
contribution of which can be significant.
It can be seen from equation (1) that at the intro-
duced power into the discharge, the consideration of
radiation will affect the corresponding distributions of
the transport coefficients, namely: electrical and thermal
conductivity. At the known temperature and the value of
the electric field strength (which are preliminary ex-
perimentally determined), the behaviour of these coeffi-
cients can be analysed. As follows from [7], the thermal
conductivity of plasma weakly depends on admixtures
of electrode origin and insignificantly differs from the
thermal conductivity of pure air. However, it was found
[7] that the electrical conductivity of plasma increases
significantly with the addition of copper, which is ex-
plained by its relatively low ionization potential. There-
fore, the thermal conductivity of pure air was used in
the calculation of the plasma electrical conductivity by
equation (1) in this work.
Plasma temperature was experimentally determined
by Boltzmann plots technique. The temperature profile
obtained in such manner is not a smooth function. This
is primarily a consequence of the application of the
Abel integral transform, which is performed by the
Bockasten method at 10 points [8]. This circumstance is
critical for equation (1), because it assumes finding the
ISSN 1562-6016. ВАНТ. 2021. № 4(134) 158
first and second derivatives of the temperature distribu-
tion. Therefore, in this work, the temperature distribu-
tion was always approximated by a smooth function
before substitution into equation (1). As can be seen
from Fig. 1 gives a good result approximation of the
Gaussian function with parameter w of the form:
2
2
0 0 .
r
w
maxT r T T T e
(2)
The obvious advantage of the approximation of the
form (2) is the yield to ambient temperature T0 at sig-
nificant distances r from the discharge and zero value of
the first derivative on the discharge axis, where
Tr=0 = Tmax.
The plasma temperature between Cu-C electrodes,
determined by Boltzmann plots technique, and its ap-
proximation by the Gaussian function of the form (2)
are shown in Fig. 1.
Fig. 1. Plasma temperature distribution of electric arc
discharge at a current of 30 A between composite Cu-C
electrodes and its approximation
by the Gaussian function
Fig. 2. Electric field strength of the positive column
(black curve) and the oscillogram of arc voltage
(grey curve) of plasma of discharge at current
of 30 A between composite Cu-C electrodes in the air
The temporal evolution of the electric field strength
of the positive column [9] and the voltage drop of arc
discharge at current of 30 A are shown in Fig. 2. One
can see, the electric field strength of arc discharge be-
tween composite Cu-C electrodes is 1.5 V/mm.
2. METHOD OF RADIATION POWER
ESTIMATION
At the first stage, determination of the electron den-
sity from the electrical conductivity of the plasma is
considered. The distribution of electrical conductivity
can be expressed from equation (1) in the form:
2 2
1 .
dT r rdr r r
rE dr dr E
(3)
On the other hand, the electrical conductivity of
plasma can be written as:
.e er eN r r (4)
After some transformations described in [10], equa-
tions (3) and (4) can be expressed as follows:
2
0
2 ,e el
e p e p el el
p e
m r EN r N Q E f E
e m
(5)
where Np is the concentration of particles of grade “p”,
Qe-p is a cross section of electron scattering on particles
of a grade “p”, f(Eel) is a Maxwell energy distribution
function of electrons.
Within the frameof this work, the scattering of elec-
trons by neutral plasma particles N2, N, O2, O, NO is
taken into account.
The radiation power density ρ(r) of the arc discharge
can be estimated indirectly at the obtained plasma tem-
perature distribution T(r). Assuming that all atomic and
molecular levels in plasma are populated according to
the Boltzmann law, the power density of particles (at-
oms, molecules, ions and molecular ions) of a corre-
sponding grade "A" can be obtained by summing the
intensity of all spectral lines, spectroscopic constants of
which are described in the literature [11 - 15]:
,
k
B
E
k T rA
A ki k ki
kA
hNr A g e
Z
(6)
where ρA(r) is the radiation power density of particles of
grade “A”, h is the Planck constant, NA is the concentra-
tion of particles of grade “A”, Aki is the Einstein coeffi-
cient of spontaneous radiation, gk is the statistical
weight of the level from which the radiation transition
occurs, νki is a photon frequency, Ek is the energy of the
upper level from which the transition takes place, kB is
the Boltzmann constant, ZA is the partition function of
the particle of grade “A”. The concentration of particles
of grade “A” is the only unknown parameter in equation
(6). The qualitative content of plasma is known in ad-
vance, and the quantitative can be calculated by the
method described in previous work [17], based on the
temperature and electron density distributions.
Therefore, at the initial stage the electrical conduc-
tivity (1) and electron density (5) are obtained without
taking into account the plasma radiation. The obtained
value of the electron density is used to calculate the
plasma equilibrium composition [17] in the next step.
Having the obtained concentration distributions of all
plasma components, its radiation can be calculated from
equation (6). At the next stage, the obtained radiation
distribution is substituted into equation (1) and the elec-
trical conductivity of the plasma is calculated taking
into account the radiation. The resulting corrected elec-
ISSN 1562-6016. ВАНТ. 2021. № 4(134) 159
trical conductivity is used to determine the actual elec-
tron density from equation (5).
3. RESULTS AND DISCUSSIONS
The radial distribution of plasma conductivity with-
out taking into account radiation was calculated (Fig. 3,
■-curve), based on the temperature distribution (see
Fig. 1) and the value of the electric field strength from
equation (3). The distribution of plasma current density
without taking into account radiation is shown in Fig. 4
(■-curve).
The total current is calculated according to the ex-
pression:
0
2 .
maxR
I E r r dr (7)
The calculated to a radius of Rmax = 4.7 mm the total
current is 19 A, although the actual discharge current is
30 A.
Fig. 3. The radial distribution of the electrical conduc-
tivity of electric arc plasma at a current of 30 A between
composite Cu-C electrodes, calculated without (■)
and with (□) taking into account the radiation
Fig. 4. Radial distribution of plasma current density
of electric arc discharge at arc current of 30 A between
composite Cu-C electrodes, calculated without (■)
and with (□) taking into account the radiation
The electron density, calculated from the distribution
of the electrical conductivity of plasma (without taking
into account the radiation) by equation (5), is shown in
Fig. 5 (■-curve). Based on the temperature and electron
density distributions (obtained without taking into ac-
count the radiation), the component composition of the
plasma was calculated and shown in Fig. 6. It was used
to obtain the plasma radiation power density by equa-
tion (6). Its radial distribution is shown in Fig. 7. In the
next step, the electrical conductivity of the plasma is
calculated by equation (3) taking into account the con-
tribution of radiation, shown in Fig. 7. The electrical
conductivity distribution of arc discharge plasma at a
current of 30 A between composite Cu-C electrodes is
shown in Fig. 3 (□-curve). The corresponding current
density distribution is shown in Fig. 4 (□-curve).
Fig. 5. Radial distribution of electron density of electric
arc discharge plasma at current of 30 A between
composite Cu-C electrodes, calculated without (■)
and with (□) taking into account the radiation
Fig. 6. Radial distribution of equilibrium plasma com-
position of electric arc discharge at current of 30 A
between the composite Cu-C electrodes
The total current of the arc discharge, calculated by
equation (7) to a radius of 4.7 mm, is 27 A, which is
much closer to the real (30 A) compared to the case
without taking into account the radiation (19 A). Using
the distribution of the electrical conductivity of the
plasma, taking into account the radiation, the equation
(5) was used to calculate the distribution of the electron
density of plasma taking into account the radiation (see
Fig. 7, □-curve). Additionally, Fig. 7 shows the distribu-
tion of heat transfer in the plasma calculated as σE2,
where the electrical conductivity is used, taking into
account the radiation. As one can see from Fig. 7, on the
axis of the discharge the radiation energy is 27% of heat
transfer and can no longer be neglected.
The arc discharge plasma between Cu-C electrodes
contains air derivatives, atoms and ions of elements of
electrode origin and various possible compounds of
these elements with air components.
ISSN 1562-6016. ВАНТ. 2021. № 4(134) 160
Fig. 7. Radial distribution of density of radiation power
of electric arc discharge plasma at current of 30 A
between composite Cu-C electrodes (□) and density
of heat transferσE2in plasma (○)
Fig. 8. Temperature dependence of radiation power
per one atom/ion
However, only the following plasma components are
taken into account in this work: O2, O, O+, N2, N, N+,
O2
+, N2
+, NO, NO+, Cu, Cu+, C, C+. Other components
of plasma are considered insignificant due to their low
concentration and high ionization potential. Although
the plasma of the electric arc discharge between com-
posite Cu-C electrodes (similarly to the plasma between
copper electrodes) contains a large number of different
particles, the main contribution to the radiation is con-
tributed by copper atoms. This is illustrated by the de-
pendence of the radiation power per one atom/ion
(Fig. 8) calculated by equation (6) for atoms of copper,
carbon, nitrogen, oxygen and copper ion. This peculiar-
ity is explained by the structure of atomic (ionic) levels.
Therefore, to estimate the radiation in this case, only
copper atoms can be considered. It should be noted, that
the emission of molecular bands were not considered in
this work. However, it can play significant role and
should be under careful study in the future investiga-
tions.
CONCLUSIONS
The distributions of electrical conductivity and elec-
tron density were obtained by the estimation of the
energy balance of the positive column of electric arc
discharge between Cu-C composite electrodes. The role
of radiation energy losses was estimated and taken into
account in the Elenbaas-Heller equation.
It was found that the total current of the arc dis-
charge with taking into account radiation was as close
as possible to the real one, compared to the case with
excluding radiation.
Additionally, it was found that the radiation energy
is 27% of heat transfer on the axis of the discharge at
arc current of 30 A, and it cannot be neglected.
ACKNOWLEDGEMENTS
This work has been carried out within the frame-
work of the EURO fusion Consortium and has received
funding from the Euratom research and training pro-
gramme 2014-2018 and 2019-2020 under grant agree-
ment No 633053. The views and opinions expressed
herein do not necessarily reflect those of the European
Commission.
In addition, authors are grateful to the partial support
of these studies in the frame of project 19БФ052-02 of
MES of Ukraine: “Investigation of properties of low-
temperature gas-discharge plasma for technological
applications”.
The authors also express their gratitude to Ministry
of Education and Science of Ukraine for the support of
project 21БП052-01 “Applications of electric discharge
plasma with condensed dispersed phase”.
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Article received 14.06.2021
ОЦЕНКА РОЛИ ИЗЛУЧЕНИЯ В ПЛАЗМЕ ЭЛЕКТРОДУГОВОГО РАЗРЯДА
МЕЖДУ КОМПОЗИТАМИ Cu-C
А. Веклич, С. Фесенко, А. Мурманцев, В. Борецкий
Работа посвящена исследованию излучения в плазме электродугового разряда между композитными Cu-
C-электродами, а также оценке его вклада при определении электронной концентрации из уравнения энер-
гетического баланса (Эленбаaса-Геллера). Также оценивается вклад энергии излучения в процессы теплооб-
мена. Расчет проводится на основе предварительно экспериментально полученного радиального распреде-
ления температуры плазмы. Для корректного решения уравнения баланса энергии используется аппрокси-
мация профиля температуры плазмы функцией Гаусса. Оценка полного тока используется в качестве крите-
рия необходимости учета излучения в диагностике плазмы электрической дуги.
ОЦІНКА РОЛІ ВИПРОМІНЮВАННЯ В ПЛАЗМІ ЕЛЕКТРОДУГОВОГО РОЗРЯДУ
МІЖ КОМПОЗИТАМИ Cu-C
А. Веклич, С. Фесенко, О. Мурманцев, В. Борецький
Робота присвячена дослідженню випромінювання в плазмі дугового розряду між композитними
Cu-C електродами та оцінці його внеску при визначенні електронної концентрації з рівняння енергетичного
балансу (Еленбааса-Геллера). Також оцінюється внесок енергії випромінювання в процеси теплообміну.
Розрахунок проводиться на основі попередньо експериментально отриманого радіального розподілу темпе-
ратури плазми. Для коректного розв’язання рівняння енергетичного балансу використовується апроксимація
профілю температури плазми функцією Гаусса. Оцінка загального струму використовується як критерій
необхідності врахування випромінювання в діагностиці плазми електричної дуги.
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