Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge
Gas-dynamic expansion of a low-energy atmospheric pressure spark discharge was numerically simulated. The calculated data were compared with experimental results to validate the numerical model. A satisfactory correlation of spark photo images with a simulated spark channel expansion was observed....
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| Zitieren: | Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge / K.V. Korytchenko, V.S. Markov, I.V. Polyakov, E.D. Slepuzhnikov, R.G. Meleshchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 144-149. — Бібліогр.: 12 назв. — англ. |
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irk-123456789-1473502019-02-15T01:23:46Z Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge Korytchenko, K.V. Markov, V.S. Polyakov, I.V. Slepuzhnikov, E.D. Meleshchenko, R.G. Плазменно-пучковый разряд, газовый разряд и плазмохимия Gas-dynamic expansion of a low-energy atmospheric pressure spark discharge was numerically simulated. The calculated data were compared with experimental results to validate the numerical model. A satisfactory correlation of spark photo images with a simulated spark channel expansion was observed. It was found out that an experimental total light intensity of spark discharge corresponds with spark radiation power. Time histories of a particle number concentration and energy input were calculated. Radial temperature, pressure, density and conductivity profiles at various times were investigated Чисельно досліджено газодинамічне розширення низькоенергетичного іскрового розряду атмосферного тиску. Перевірка математичної моделі проведена шляхом порівняння чисельних та експериментальних результатів. Отримана задовільна кореляція фотозображень іскрового розряду з розрахунковими даними з розширення іскрового каналу. З’ясовано, що повна інтенсивність випромінювання іскрового розряду, яка отримана експериментально, відповідає потужності випромінювання іскри. Розраховано розподіл концентрації компонентів та динаміка вводу енергії в іскру. Досліджені розподіли температури, тиску, густини та провідності в радіальному розрізі в різні моменти часу. Численно исследовано газодинамическое расширение низкоэнергетического искрового разряда атмосферного давления. Проверка математической модели проведена путем сравнения численных и экспериментальных результатов. Получена удовлетворительная корреляция фотоизображений искрового разряда с расчетными данными по расширению искрового канала. Выявлено, что полная интенсивность излучения искрового разряда, получаемая экспериментально, соответствует мощности излучения искры. Рассчитано распределение концентрации компонентов и динамика ввода энергии в искру. Исследованы распределения температуры, давления, плотности и проводимости в радиальном сечении в разные моменты времени. 2018 Article Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge / K.V. Korytchenko, V.S. Markov, I.V. Polyakov, E.D. Slepuzhnikov, R.G. Meleshchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 144-149. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 52.80.Mg http://dspace.nbuv.gov.ua/handle/123456789/147350 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| spellingShingle |
Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Korytchenko, K.V. Markov, V.S. Polyakov, I.V. Slepuzhnikov, E.D. Meleshchenko, R.G. Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge Вопросы атомной науки и техники |
| description |
Gas-dynamic expansion of a low-energy atmospheric pressure spark discharge was numerically simulated. The
calculated data were compared with experimental results to validate the numerical model. A satisfactory correlation
of spark photo images with a simulated spark channel expansion was observed. It was found out that an experimental
total light intensity of spark discharge corresponds with spark radiation power. Time histories of a particle number
concentration and energy input were calculated. Radial temperature, pressure, density and conductivity profiles at
various times were investigated |
| format |
Article |
| author |
Korytchenko, K.V. Markov, V.S. Polyakov, I.V. Slepuzhnikov, E.D. Meleshchenko, R.G. |
| author_facet |
Korytchenko, K.V. Markov, V.S. Polyakov, I.V. Slepuzhnikov, E.D. Meleshchenko, R.G. |
| author_sort |
Korytchenko, K.V. |
| title |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| title_short |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| title_full |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| title_fullStr |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| title_full_unstemmed |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| title_sort |
validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2018 |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147350 |
| citation_txt |
Validation of the numerical model of a spark channel expansion in a low-energy atmospheric pressure discharge / K.V. Korytchenko, V.S. Markov, I.V. Polyakov, E.D. Slepuzhnikov, R.G. Meleshchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 144-149. — Бібліогр.: 12 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-11T02:16:23Z |
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2025-07-11T02:16:23Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 144
VALIDATION OF THE NUMERICAL MODEL OF A SPARK
CHANNEL EXPANSION IN A LOW-ENERGY
ATMOSPHERIC PRESSURE DISCHARGE
K.V. Korytchenko1, V.S. Markov1, I.V. Polyakov1, E.D. Slepuzhnikov2, R.G. Meleshchenko2
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
E-mail: omsroot@kpi.kharkov.ua;
2National University of Civil Defence of Ukraine, Kharkоv, Ukraine
E-mail: korytchenko_kv@ukr.net
Gas-dynamic expansion of a low-energy atmospheric pressure spark discharge was numerically simulated. The
calculated data were compared with experimental results to validate the numerical model. A satisfactory correlation
of spark photo images with a simulated spark channel expansion was observed. It was found out that an experimental
total light intensity of spark discharge corresponds with spark radiation power. Time histories of a particle number
concentration and energy input were calculated. Radial temperature, pressure, density and conductivity profiles at
various times were investigated.
PACS: 52.80.Mg
INTRODUCTION
A spark discharge has a lot of fields of using. For
example, it applied for ignition of a combustible mixture
including a direct detonation initiation, lighting, electri-
cal switching, nanoparticle generation, etc. A complex
experimental investigation of spark discharges requires
high resolution techniques to measure a spark channel
evolution, generated shock wave expansion, chemical
components concentration distributions, light intensity,
spatial distribution of temperature, pressure, density in
spark channel, efficiency of energy deposition, excitation
of discharge components, changing in electrical features
(conductivity, voltage falling), etc [1 - 3]. Thus experi-
mental spark researches are extremely complicated.
The numerical model of a spark discharge which is
convenient for application was recently developed [4 -
6]. A specific feature of the model is its ability to predict
a spark channel expansion in the gas when electric cir-
cuit parameters, the discharge gap length, and initial
thermodynamic gas state are given.
It is important to determine conditions of the model
application. The model was successfully validated pre-
viously by a high-energy spark discharge where the total
spark energy equals about tens of Joules [7]. Now we
validate the model when the total discharge energy is
below one Joule.
We used experimental data of a channel expansion
of a low-energy atmospheric pressure spark discharge in
nitrogen [1]. The experimental data include as a time-
resolved imaging as electrical study of the discharge.
Thus, the capacitance, resistance and inductance of a
serial RLC-circuit, the length of the discharge gap and
initial thermodynamic state of the discharge gas were
used as initial conditions in the numerical model. Then
we compared the experimental and simulated results of
the channel expansion and the total light intensity to
validate the model.
THE NUMERICAL MODEL
OF A SPARK CHANNEL EXPANSION
Detailed description of the numerical model is given
in [4 - 7]. The model can be applied to simulate a spark
evolution after breakdown when the initial current-
conducting channel is formed. The model describes a
spark stage of a gas-dynamic expansion.
The setup was simplified to a one-dimensional prob-
lem in cylindrical symmetry where only radial depend-
encies were modelled. A system of gas dynamic equa-
tions (continuity, momentum and energy) was solved for
the multicomponent chemically reactive gas mixture
(molecular and atomic nitrogen), written as
0)(1
=
∂
ρ∂
+
∂
ρ∂
r
ur
rt
; (1)
( )[ ]
r
p
r
upr
rt
u
=
∂
ρ+∂
+
∂
ρ∂ 21 ; (2)
;2
21
em
2
2
2
WE
t
u
r
dt
dTkpuur
r
T
−σ=
∂
ρ
+ρe∂
+
+
∂
+
+
ρ
+ρe∂
(3)
i
ii
r
ruy
rt
y
ω=
∂
∂
+
∂
∂ )(1 , (4)
where ρ is the gas density; u is the velocity, p is the
pressure, e is the internal energy of gas per the mass unit
of gas, kТ is the heat conduction coefficient, E is the
electric field strength in the discharge channel column, σ
is the plasma conductivity in the channel, Wem is the
discharge energy radiation loss, r is the radial coordi-
nate, t is the time, T is the gas temperature, yi is the mo-
lar concentration of the i-th component (N2, N), and ωi is
the rate of change of concentration of the i-th compo-
nent of the mixture due to chemical reactions.
We applied equations of a local thermodynamic
equilibrium (LTE) plasma state to find out plasma pa-
rameters in a spark discharge conductive channel. Con-
ditions of LTE-model application were checked. In the
conductive channel components e, N, N+, N++ have been
considered. In the calculated region outside the conduc-
tive channel plasma ionization has been neglected. In
this region the components N2, N have been considered.
ISSN 1562-6016. ВАНТ. 2018. №4(116) 145
We used equations of non-equilibrium chemical reac-
tions to calculate components concentration in this re-
gion. The energy deposition in the discharge channel
was defined by the parameters of electric circuit. The
diffusion process was not taken into account.
To calculate the Joule heat deposited into the dis-
charge channel we are supposed to know the current
values of the electric field strength Е in the discharge
channel column and plasma conductivity distribution σ
in the plasma channel. It was assumed that only a longi-
tudinal component of the electric field is present in the
discharge channel and the field is uniformly distributed
across the channel cross-section.
The conductivity distribution in the gas-discharge
channel was considered proceeding from the channel-
based problem formulation. The highly ionized region
was defined from the condition of tenfold exceed of the
frequency of Coulomb collisions in comparison with
that of elastic collision of electrons with a neutral plas-
ma component (N atoms) as follows [8]
10
olСe
tr
nN σ⋅
≤σ⋅ , (5)
where σtr is the transport cross-section of elastic colli-
sions of electrons with a neutral plasma component, N is
the neutral plasma component density; ne is the electron
number density, σCol is the Coulomb collision cross-
section.
It was assumed for the model that plasma in a dis-
charge channel is quasi neutral with the ionization de-
gree not exceeding a double one. An electron attachment
process was neglected in the model.
The ionization in the discharge channel was calculated
using the Saha equation with regard to the single and dou-
ble ionization of gas with components of e, N, N+, N++.
The electron density ne and plasma temperature in rated
cells were defined by solving the equation system:
)exp(2
3
kT
eITA
g
g
N
nn N
N
N
N
Ne +++ −⋅= ; (6)
)exp(2
3
kT
eITA
g
g
n
nn N
N
N
N
Ne ++
+
++
+
++ −⋅= ; (7)
2/)(
)(
2
3
NNNNNN
NNeNNN
InnNeIn
eInkTnnnN
+++++++
+++++
++++
+++++=e
; (8)
+++ += NNe nnn 2 ; (9)
m.i.aNNNNN mZ)nnN( +++ ++=ρ ; (10)
where А = 6.06·10-21 cm-3eV-3/2; gi are the degeneracy of
state for the ion i; IN is the nitrogen molecule dissocia-
tion energy; IN+, IN++ is the energy of single and double
ionization of nitrogen atom; ZN is the mass number of
nitrogen; mа.i.m. = 1.66·10-27 kg; ρN is the atomic nitrogen
density, e is the electron charge, ne is the electron num-
ber density; n+ is the single ionization atom number den-
sity; n++ is the double ionization atom number density,
NN is the number density of atomic nitrogen, k is the
Boltzman constant.
The degeneracy of state for the ion gi and ionization
energy of Ii components were taken from [9]. The plasma
conductivity was calculated using the equation [10]
Λ
⋅⋅
=σ σ
ln
)(994.96),(
2/3TZKTZ [Ω-1cm-1], (11)
where Кσ(Z) is the dimensionless coefficient; Z is the
average ion charge; lnΛ is the Coulomb logarithm.
In the region of strongly ionized plasma (conductive
channel) the gas pressure p was calculated using the
expression
kTnnnNp e )( +++ +++= . (12)
Resistance Rsp of the discharge channel for the cur-
rent time point was defined by the integration of current
conductivity values σ in rated cells using the expression
∫ σπ=
chr
spsp drrlR
0
2/ , (13)
where lsp is the discharge gap length (channel); rch is the
conductive channel radius.
The electric field strength Е was calculated using the
expression
spsp liRE /= . (14)
The electrical process in the series RLC circuit was
calculated using the equation
[ ] ∫ =+⋅++
t
spc idt
C
itRR
dt
diL
0
01)( , (15)
where С is the capacitor capacitance, Rc is the equiva-
lent ohmic resistance of a discharge circuit; L is the
equivalent inductance of a discharge circuit.
The radiation discharge energy losses were calculat-
ed using the expression
RSBem lТW /4σ= , (16)
where σSB is the Stefan–Boltzmann constant, lR is the
Rosseland mean free path.
The dissociation/association process in nitrogen gas
was calculated by reaction (Table). The velocity con-
stant of the chemical reaction is expressed as
−=
RT
ETAk akkn
kk exp , (17)
where R is the gas constant.
The coefficients of the velocity constants
of forward reactions and the activation energy,
adopted for the model
REACTION Аk nk Eak
N2 + M ↔ N + N + M 8.508·1025 -2.5 225
Remark. Where M denotes the third particle.
The values are expressed in calories, moles, сm3, and s
The reverse rate coefficient was calculated from the
forward rate and the equilibrium constant.
Specific heat capacity at constant pressure, standard-
state molar enthalpy and standard-state molar entropy
component (N2, N) as a function of a temperature T in
the range of 300 to 5000 К were calculated as in [12].
The energy of the unit of mixture volume U0 was pre-
scribed by the expression of
∑=ρe
k
kkUy 0 , (18)
where yk is the molecular concentration of the k-th com-
ponent of mixture, Uk
0 is the internal energy of 1 mole
of the k-th component.
A mixture pressure in the cells outside the conduc-
tive channel was calculated using the sum of partial
ISSN 1562-6016. ВАНТ. 2018. №4(116) 146
pressures of mixture components. The gradients of
thermodynamic gas parameters are assumed to be absent
for the discharge channel axis in a cylindrical symmetry.
The computational area size was prescribed in the man-
ner of preventing disturbance from reaching the right
boundary. It is assumed that initial conditions have no
gas dynamic perturbations in the entire computation
region. For the computations given below it is assumed
that р0 = 1.013·105 Pa, Т0 = 300 К. For initial conditions
the computation region was filled with molecular nitro-
gen. The model requires a circuit shorting to start simu-
lating. So we manually inputted an energy in the simu-
lated region with a radius of r0 = 50 μm during a time of
t = 10 ns to form a narrow current-conducting channel.
This energy was 0.24 mJ.
RESULTS OF A NUMERICAL SIMULATION
OF A SPARK EXPANSION
It is accustomed getting the schlieren images to in-
vestigate a spark channel expansion [3]. The Schlieren
images show a spatial distribution of density gradient
that allows being visible as a channel as a shock wave
due to density changing in the channel and the wave
during a spark evolution. The photo images taken from
work [1] show a spatial distribution of lighting intensity
in spark discharge. It is known [8] that a high-
temperature spark channel produces the lighting. Thus
we compared the photo images with the radial tempera-
ture profiles of a spark discharge in this work. We used
the photo imaging results for flat-end electrodes because
this data better corresponds to a one-dimensional simu-
lation in cylindrical symmetry assumed in our model.
The length of the spark gap l equaled 2 mm in the calcu-
lation that corresponds to the experimental condition of
the shooting.
The parameters of a serial RLC circuit used in [1]
were analyzed carefully. We applied a capacitor bank
with a total capacitance of C = 29 nF and inductance of
L = 3.6 μH in the calculation. The charge voltage was
Uc = 5425 V thus the total energy was 427 mJ. Accord-
ing to estimation presented in [1], the total resistance
values were in the range of 1.30…1.65 Ω. Using the
measured current signal and simulating a current curve
for such a RLC circuit where the resistance was
R = 1.65 Ω we found out that there is a correlation of
the current curves in third period of discharge (Fig. 1).
Initially we assumed that the resistance value of
1.65 Ω is the equivalent ohmic resistance of discharge
circuit. And the current reducing happened due to an
additional resistance of a spark discharge.
Fig. 1. Experimental current signal [1] (solid curve)
and calculated current (dotted curve) for Rc = 1.65 Ω
But our simulated data obtained by taking into ac-
count the spark resistance showed that the calculated
amplitude of a discharge current exceeded the experi-
mental amplitude in this case. Current difference was
above 100 A. Moreover, we observed that the simulated
current-conducting channel expanded faster than the
measured spark channel. For example, a comparison
between the image at 2750 ns and radial temperature
profile at 2000 ns is given (Fig. 2).
Fig. 2. Experimental images of the spark at 2750 ns
and calculated radial temperature profile at 2000 ns
So the ohmic resistance was adapted in such a way
that we had a satisfactory correlation of the measured
discharge current with the simulated current. The ohmic
resistance was variable. The resistance was presented by
function of time (Fig. 3).
Fig. 3. Time dependence of the ohmic resistance
adapted for the calculation
It is known [3] that there is a voltage drop in anode
and cathode zones that is variable during a spark evolu-
tion. Thus the time variable ohmic resistance can be
caused by a process connected with discharge elec-
trodes.
A comparison of the experimental and calculated
discharge currents is presented (Fig. 4).
Fig. 4. Experimental [1] (on the left) and simulated
(on the right) spark current
ISSN 1562-6016. ВАНТ. 2018. №4(116) 147
The numerical simulation showed that the photo im-
ages of spark discharge present the evolution of high-
temperature region of the discharge where gas tempera-
ture exceeds 10000 K (Figs. 5-7).
Fig. 5. Experimental image of the spark (upper) and
calculated radial temperature profile (below) at 50 ns
Fig. 6. Experimental image of the spark (upper) and
calculated radial temperature profile (below) at 600 ns
Fig. 7. Experimental image [1] of the spark (upper) and
calculated radial temperature profile (below) at 2750 ns
There is temperature growth behind shock wave that
is not visible in the images. The temperature rises in the
range of 460…500 K behind the shock wave at 2750 ns
(see Fig. 5). It is known [8] that when gas temperature is
slightly higher than room temperature, gas has a specific
absorption/emission spectrum. Thus the temperature
growth caused by the wave is not visible because the
preheated gas does not have visible spectrum.
The comparisons show that we have a satisfactory
agreement between experiment and theory.
Radiant energy of the investigated discharge was
calculated (Fig. 8).
Fig. 8. Simulated time history of radiant energy
Then we differentiated the radiant energy with re-
spect to time to calculate radiant power. As a result we
clarified that normalized intensity obtained in work [1]
corresponds to the spark radiant power. A maximum of
the power exceeds 1.5 kW (Fig. 9).
Practically the same evolution of spark channel radi-
uses we have in experimental and calculated cases
(Fig. 10). There is a slight difference at initial time of
the channel expansion. It is known [8] that there is a
spark process of current contraction happens after
breakdown. We think a time resolution of an experi-
mental setup did not allow catching a contraction pro-
cess.
The numerical model allows investigating a time his-
tory of a particle number concentration (Fig. 11). These
results can be useful to check the model using specific
experimental equipment.
Fig. 9. Comparison of experimental intensity
of lighting [1] (curve № 1)
and calculated radiation power (curve № 2)
ISSN 1562-6016. ВАНТ. 2018. №4(116) 148
Fig. 10. Comparison of evolutions of spark channel
radius in experimental [1] (on the left)
and calculated (on the right) cases
Fig. 11. The simulated radial profiles of a particle num-
ber concentration in the spark discharge at 2750 ns
A time variation of a spark resistance was calculated
(Fig 12). It was found out that the spark resistance in
0.2…0.3 μs falls below 1 Ω.
Fig. 12. The time variation of the spark resistance
Fig. 13. The simulated radial pressure profiles
atvarious times
Fig. 14. The radial density profiles at various times
Fig. 15. The radial conductivity profiles
at various times
It is a reason that the spark resistance weakly influ-
ences the discharge current in the considered case.
There is a technical problem to get experimental meas-
urements of pressure, density and conductivity in spark
discharges at various times. We presented the simulated
data of these values (Figs. 13-15).
For example, the pressure data can be useful to pre-
dict pressure affect in a capillary discharge. As for other
data, it is possible to detach a current-conducting chan-
nel from a shock wave via comparison of the conductivi-
ty and pressure profiles at the same time.
It is known [8] that spark energy efficiency is varia-
ble. The efficiency depends on total discharge energy,
electrical circuit parameters, a length of a spark gap, and
an initial thermodynamic gas state in discharge, etc. The
designed model allows finding out energy inputted in a
spark channel (Fig. 16).
Fig. 16. The simulated time history of energy
input in spark discharge
We calculated that an intensive energy input happens
at first period of discharge. The efficiency exceeds 8%
in considered case.
CONCLUSIONS
A satisfactory correlation between spark photo im-
ages and simulated radial temperature profiles at various
times confirmed that the designed numerical model of a
spark evolution can be applied when the total discharge
energy is below one Joule.
REFERENCES
1. J. M. Palomares, A. Kohut, G. Galbács, R. Engeln,
and Zs. Geretovszky. A time-resolved imaging and
electrical study on a high current atmospheric pres-
sure spark discharge // Journal of Applied Physics.
2015, v. 118, p. 233305.
2. S. Essmann, D. Markus, U. Maas. Investigation of
the spark channel of electrical discharges near the
ISSN 1562-6016. ВАНТ. 2018. №4(116) 149
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Article received 01.06.2018
ПРОВЕРКА МАТЕМАТИЧЕСКОЙ МОДЕЛИ РАСШИРЕНИЯ ИСКРОВОГО КАНАЛА
НИЗКОЭНЕРГЕТИЧНОГО РАЗРЯДА АТМОСФЕРНОГО ДАВЛЕНИЯ
К.В. Корытченко, В.С. Mарков, И.В. Поляков, Е.Д. Слепужников, Р.Г. Mелещенко
Численно исследовано газодинамическое расширение низкоэнергетического искрового разряда атмо-
сферного давления. Проверка математической модели проведена путем сравнения численных и эксперимен-
тальных результатов. Получена удовлетворительная корреляция фотоизображений искрового разряда с рас-
четными данными по расширению искрового канала. Выявлено, что полная интенсивность излучения искро-
вого разряда, получаемая экспериментально, соответствует мощности излучения искры. Рассчитано распре-
деление концентрации компонентов и динамика ввода энергии в искру. Исследованы распределения темпе-
ратуры, давления, плотности и проводимости в радиальном сечении в разные моменты времени.
ПЕРЕВІРКА МАТЕМАТИЧНОЇ МОДЕЛІ РОЗШИРЕННЯ ІСКРОВОГО КАНАЛУ
НИЗЬКОЕНЕРГЕТИЧНОГО РОЗРЯДУ АТМОСФЕРНОГО ТИСКУ
К.В. Коритченко, В.С. Maрков, I.В. Поляков, Є.Д. Слепужніков, Р.Г. Meлещенко
Чисельно досліджено газодинамічне розширення низькоенергетичного іскрового розряду атмосферного
тиску. Перевірка математичної моделі проведена шляхом порівняння чисельних та експериментальних ре-
зультатів. Отримана задовільна кореляція фотозображень іскрового розряду з розрахунковими даними з ро-
зширення іскрового каналу. З’ясовано, що повна інтенсивність випромінювання іскрового розряду, яка
отримана експериментально, відповідає потужності випромінювання іскри. Розраховано розподіл концент-
рації компонентів та динаміка вводу енергії в іскру. Досліджені розподіли температури, тиску, густини та
провідності в радіальному розрізі в різні моменти часу.
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