Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production
In this paper as a result of the theoretical studies and a numerical simulation we presented the following main conclusions: (i) for humid air at increasing pressure of 1.0133 10⁵ Pa until 5.0665 10⁵ Pa ozone concentrations during 2·10⁻³s become higher in 22 times. This fact we clear with structure...
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| Date: | 2003 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Cite this: | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production / V.I. Karas', V.I. Golota, V.P. Mal'khanov, I.F. Potapenko, O.N. Shulika // Вопросы атомной науки и техники. — 2003. — № 4. — С. 247-253. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859520108410437632 |
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| author | Karas', V.I. Golota, V.I. Mal'khanov, V.P. Potapenko, I.F. Shulika, O.N. |
| author_facet | Karas', V.I. Golota, V.I. Mal'khanov, V.P. Potapenko, I.F. Shulika, O.N. |
| citation_txt | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production / V.I. Karas', V.I. Golota, V.P. Mal'khanov, I.F. Potapenko, O.N. Shulika // Вопросы атомной науки и техники. — 2003. — № 4. — С. 247-253. — Бібліогр.: 6 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | In this paper as a result of the theoretical studies and a numerical simulation we presented the following main conclusions: (i) for humid air at increasing pressure of 1.0133 10⁵ Pa until 5.0665 10⁵ Pa ozone concentrations during 2·10⁻³s become higher in 22 times. This fact we clear with structure of ozone-production reactions. In this case the harmful NOx concentrations are 2-3 order lower than ozone one; (ii) it is shown that nitrogen is useful to ozone production in the discharge; (iii) based on ion collection we cleared increasing ignition discharge voltage at growing ozone concentrations even with low ozone concentrations.
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UDK 533.9
THEORETICAL STUDY OF THE NON-STEADY DISCHARGE AT AT-
MOSPHERIC PRESSURE IN PIN - PLATE SYSTEM AND ITS APPLICA-
TION FOR OZONE PRODUCTION
V.I. Karas'1, V.I. Golota1, V.P. Mal'khanov2, I.F. Potapenko3, O.N. Shulika1
1National Science Center "Kharkov Institute of Physics & Technology", Kharkov, Ukraine,
karas@kipt.kharkov.ua, fax: 38(0572)353564
2TurboDEn, Moscow, Russia, turboden@mail.ru, fax: 7(095)4680332
3Keldysh Institute of Applied Mathematics of the RAS, Moscow, Russia, irina@KELDYSH.ru,
fax: 7(095)9720737
In this paper as a result of the theoretical studies and a numerical simulation we presented the following main
conclusions: (i) for humid air at increasing pressure of 1.0133 105 Pa until 5.0665 105 Pa ozone concentrations dur-
ing 2·10-3s become higher in 22 times. This fact we clear with structure of ozone-production reactions. In this case
the harmful xNO concentrations are 2-3 order lower than ozone one; (ii) it is shown that nitrogen is useful to ozone
production in the discharge; (iii) based on ion collection we cleared increasing ignition discharge voltage at growing
ozone concentrations even with low ozone concentrations.
INTRODUCTION
Electrodynamic and plasma-chemical processes at
high-pressure glow discharge conditions have a very
complicated, many-factor character, because in the dis-
charge gap there occur nearly simultaneously a great
many separate streamer discharges, which cross the dis-
charge space parallel to each other. Generally, one can
expect that the discharge characteristics are determined
by the energy put into the gas flow. However, it is evi-
dent that the resulting gradients of the discharge param-
eters along the gas flow are not too great, because the
specific power density is not high. Therefore the varia-
tions in the gas/discharge parameters from one local
streamer discharge to another can be neglected. By con-
trast, the nonuniformity in the discharge parameters in
the direction from one electrode to the other should be
expected to be very strong. Really, the radius of current
channel near the needle is several orders of magnitude
smaller than the period of needle separation along the
gas flow. This means that the gradients of both the elec-
tric field strength and the charged particle density are
great, particularly in the vicinity of the needle electrode.
So, the two-dimensional model for the glow discharge
can be constructed by taking one PCR structure element
and formulating the equations, which describe the prop-
agation of the discharge from the needle electrode to the
plane electrode.
In atmospheric-pressure air, the nonlocality effects
of electron/ion distributions, and also, of diffusion, can
play a certain role only at a very small distance from the
electrode (cathode dark space). Bearing in mind the in-
sensibility of the parameter of the cathode layer to the
choice of the kinetic model, we have chosen the sim-
plest model, where all the transport coefficients and the
kinetic coefficients are the local-importance functions of
the reduced electric field NE ( E is the electric field
strength, N is the gas particle density).
The basic parameters of any electrical discharge in
gas are mainly determined by the energy distribution of
electrons. The knowledge of electron kinetics of the low
-temperature plasma is of great importance for simula-
tion of plasma-chemical processes in the glow discharge
in air. For example, the average energy or the tempera-
ture of electrons governs the rate of plasma-chemical
processes and the discharge power distribution between
different channels. A more exact analysis can be per-
formed with the use of the electron energy distribution
function (EEDF), but the experimental determination of
the EEDF in plasma is a rather complicated problem.
Therefore, various methods of theoretical simulation are
in considerable use. A typical theoretical approach to
determination of the EEDF in a gas plasma is the solu-
tion of the Boltzmann equation in the two-body approxi-
mation. This approach appears rather simple and reli-
able; it is confirmed by comparison with more substanti-
ated methods of simulation, e.g., the Monte-Carlo
method.
The electron motion in gas under the action of the
external electric field E is determined by the frequency
of collision with molecules and other charged particles.
The electron-electron collisions become to play a cer-
tain role at a relatively high degree of gas ionization,
generally, starting from 10-4 - 10-3. Typical electron den-
sities in the discharge are substantially less than 1015 cm-
3, therefore the electron-electron interaction can be ne-
glected to a high accuracy.
The discharge in the gas flow is simulated in the
framework of the zero-dimensional model that considers
the time evolution of charged particle motion as an evo-
lution of gas portion that is moving together with the
gas flow crosswise to the discharge gap. In this model,
air is considered as a 2N : 2O : OH 2 mixture being in
the electrical field which is calculated by solving the
equation for the electric circuit involving the electromo-
tive force source, ballast resistance and discharge. In
consequence of a rather small energy contribution to the
gas, the variations in the gas composition and vibration
temperatures can be neglected. The electron-electron,
electron-ion collisions and any other collisions of II-
type can also be neglected. In this case, all kinetic coef-
mailto:irina@KELDYSH.ru
mailto:turboden@mail.ru
mailto:karas@kipt.kharkov.ua
ficients for the processes involving electrons are the
functions of the reduced electric field NE and the gas
composition.
MATHEMATICAL SIMULATION OF KINET-
IC PROCESSES AT GLOW DISCHARGE
CONDITIONS
The mathematical model of discharge, developed
here in accordance with [2], makes it possible to calcu-
late the evolution of many important plasma compo-
nents: ions ( +
2N , +
2O , +
4O , −O , −
2O , −
3O ), electron-
excited particles ( ( )+Σ uAN 3
2 , ∗
2N , ( )∆1
2 aO , ( )Σ1
2 bO ,
( )DO 1 ), atoms ( N , O ), ozone ( 3O ), nitrogen oxides (
NO , ON2 , 2NO , 3NO , 52ON ) and electrons. Here ∗
2N
denotes the electron-excited molecule of nitrogen at any
level, except for +Σ uA3 In humid air, electrons attach to
molecules to form negative ions. The negative ions of
most importance are −O , −
2O , −
3O , −
4O , −H , −OH ,
−
2NO , −
3NO , ( )OHO 22
− , ( ) 222 OHO − , ( )OHOH 2
− and
( ) 22OHOH − .
The electron detachment from negative ions is of
great importance, because it influences the plasma con-
ductivity. At a measured average electric field strength
of ~104 V/cm in the discharge gap, the attachment rate is
appreciably higher than the electron-impact ionization
rate. The other process that leads to electron losses is
the electron-ion recombination. The only process that
can, in principle, compensate the electron losses is the
electron detachment from negative ions. The processes
of electron detachment include a simple electron detach-
ment, the associated detachment and photodetachment.
For the atmospheric plasma, the last process can be ne-
glected.
It is well known that the addition of water vapor to
any weakly ionized gas or plasma exerts a considerable
effect on the content of positive and negative ions, and
the cluster water ions become the predominant ions.
This changes the properties of a weakly ionized envi-
ronment, because (i) the process of electron detachment
from negative cluster ions proceeds very slowly, (ii) the
process of dissociative recombination of electrons with
positive cluster ions of water goes much quicker than
with simple positive ions. The both effects lead to a de-
crease in the electron density, and hence, in the degree
of ionization. Therefore, it is of importance to know the
rate constants for cluster water ion formation and break-
down.
In simulation, the processes of OH 2 molecule ion-
ization and dissociative attachment, being of greatest
importance for the plasma balance, were characterized
by the rate constants in the form of functions of the re-
duced electric field, which were calculated through the
solution of the Boltzmann equation for electrons. At a
critical reduced electric field value ( ) cNE =12.4⋅10-
16 V cm2, the processes of ionization and attachment
equalize each other. This value is often called the equi-
librium point. In the absence of detachment processes in
the collisions, the equilibrium value of the reduced elec-
tric field must be no less than ( ) cNE . The detachment
processes provide an additional amount of electrons as
if from an external ionization source, that gives the pos-
sibility to maintain the discharge burning at an electric
field lower than the equilibrium value.
The continuity equations for electrons and basic positive
and negative ions are solved with the 1D - model, that
can be briefly described as follows.
The geometry of discharge is symmetrical with re-
spect to the discharge axis. This means that the continu-
ity equation can be solved in terms of the variables
( )x r, , where x is the distance from the cathode along
the discharge axis, r is the radius. However, the solu-
tion of the two-dimensional nonstationary problem in
the physics of discharge is still a serious challenge to
computer potentialities. On the other hand, the presenta-
tion and treatment of calculations also presents difficul-
ties. The present paper deals with a quasi-one-dimen-
sional numerical model. To derive the equations of this
model, we make an assumption that all physical param-
eters ( E , ne , n p , nn ) are constants in each cross sec-
tion for the discharge current. This approximation was
used, for example, by R. Morrow [1], who assumed the
discharge channel to have the cylindrical shape. Howev-
er, from a great many experiments it is well known that
the discharge current is concentrated as a small spot on
the needle and occupies a comparatively large area on a
flat cathode. If the radius of the current channel is intro-
duced, then it strongly increases from the rod to the
plane. The ratio of current channel radii on the negative
and positive electrodes makes about 103. In agree to A.
Napartovich et al [2] we consider the radius of the cur-
rent channel to be the function of the axial coordinate x
. The problem of choosing the channel shape will be
discussed separately. Then, integrating the equation
with respect to the cylinder of radius r and height dx
and taking into account the mentioned constancy of the
physical parameters, one can obtain the following equa-
tions:
( ) ( ) ndeaiee
e nvnvvwSn
xSt
n
+−=+
∂
∂
∂
∂ 1 , (1)
( ) eipp
p nvwSn
xSt
n
=−
∂
∂
∂
∂ 1 , (2)
( ) ndeann
n nvnvwSn
xSt
n
−=+
∂
∂
∂
∂ 1 , (3)
( ) ( )
0
1
ε∂
∂ ennnSE
xS nep −−−= , (4)
where ( )S x is the cross-sectional area of the current
channel, which is considered to be the known function
of the coordinate x. The introduction of this function is
the key point of this model.
Let us discuss this approximation in greater detail. In
reality, the charged particle concentrations and the elec-
tric field strength vary in space, both along and across
the discharge axis. The assumption that these parame-
ters are the step functions of the radius and turn into
zero on the channel surface seems quite natural. Howev-
er, it can be substantiated only with a slow variation of
( )xS , i.e., at d(lnS)/d(lnx)>1. We ignore this prob-
lem assuming the channel shape close to the expected
one. The other assumption made in the construction of
equations (1) - (4) is that the current channel retains its
shape all the time. However, this is of no importance for
the corona at steady-state conditions.
Equations (1) - (4) should be supplemented by
boundary conditions. The boundary conditions for posi-
tive and negative ions are obvious: their concentrations
equal zero at the anode and at the cathode, respectively.
For electrons, in contrast to R. Morrow [1], we consider
only the secondary electron emission caused by the
ions. Really, some particular processes in air that would
yield an essential amount of secondary photoelectrons
are unknown. Therefore, it appears reasonable to ne-
glect them at all. Then the boundary condition for elec-
trons is formulated through the introduction of the sec-
ondary ion emission coefficient γ :
( ) ( )tjtj pe ,0,0 γ= , (5)
where j n we e e= , j n wp p p= .. The boundary condi-
tions for the electric field strength were determined di-
rectly from eqs. (1) - (4) at each time step. The proce-
dure and a detailed description of the numerical algo-
rithm for the solution of the set of eqs. (1)-(4) can be
found in ref. [2].
The solution of the above-described set of equations
is a complicated task because of a great difference be-
tween the characteristic times of the physical processes,
and because of the fact that the parameters to be calcu-
lated (electric field, charged particle density) strongly
vary in the space between the electrodes. For the numer-
ical solution we use the implicit numerical scheme. The
space grid is nonuniform, having a smaller step in the
vicinity of the electrodes (in particular, close to the nee-
dle tip). The integration step in time τ is limited by
three conditions:
( )( )Eeµτ ∆< min , (6)
( )ai vv 1,1min<τ , (7)
Mττ < , (8)
where ∆ is the local grid size in space, ( )π στ 41=M )
is the Maxwellian time, σ is the plasma conductivity.
To avoid the numerical instability, we put the time
dependence of the supply voltage in the following form:
( )( )supplsuppl tUU τ−−= exp9,010 , (9)
where supplτ = 20µs can be considered as a characteris-
tic time of the establishment of steady-state conditions.
If it is compared with the time intervals, for which the
calculations are made, it can be seen that except for the
very beginning, the calculations are performed with a
practically stable supply voltage, as is also the case in
experiment.
Typically, the total number of numerical grid nodes
was 160. The real time integration step ranged between
10-12 - 10-11s.
The calculations of concentrations of basic charged
components are performed by the above-described one-
dimensional model, where the equations were averaged
in the approximation of the given discharge shape, i.e.,
relying on some experimental data or some other physi-
cal concepts we assign the shape of the current channel,
over which the continuity equations are averaged. In
this case, it is also assumed that all the parameters do
not vary in the discharge cross section, but are depen-
dent only on the longitudinal coordinate. The Poisson
equation, as opposed to other approaches, is solved in
the two-dimensional space (in parabolic coordinates)
with the help of integration of the algebraic sum of
charged component concentrations using the known
Green function [6] 1−= RG :
( ) ( ) ( ) ( )∑
∞
=
∫
∞
×=
0 0 00{2
m
kdkkmKkmIkmJkmJG µµλλ
[ ])(cos 0ϕϕχ −× mm }, µµ >0 , (10)
where λ , µ are the paraboloid characteristics, mJ is
the first-order Bessel function, mI , mK are the modi-
fied Bessel functions of the imaginary argument.
The resulting from this integration spatial distribu-
tion of the potential determines the distribution of the
reduced electric field NE . The knowledge of this dis-
tribution permits the use of a locally zero-dimensional
model of chemical kinetics, which takes into account
about 100 chemical reactions, owing to the local depen-
dence of the rate constants of the main processes (ion-
ization, attachment, detachment, associative recombina-
tion, dissociative recombination, etc.), this being due to
the presence of the small parameter elb λ= (where l
is the characteristic electrode size and separation, eλ is
the free path length of the electron between the succes-
sive collisions) on account of a high pressure of the gas
mixture. The quantitative and qualitative compositions
of plasma components, between which collisions occur,
are substantially dependent on the degree of nonequilib-
rium of the system, i.e., on the appreciable excess of the
average electron energy over the energies of ions, neu-
tral molecules and atoms. Not to overload the problem,
we do not take into account the nonequilibrium in the
vibrational level distribution. This can be done at a not
too high specific power of the discharge, i.e., for the
ozonizers with a high gas flow rate as in our case.
The distribution of gas-mixture chemical compo-
nents, found at the previous stage, makes it possible to
find the space distribution of the electron distribution
function and, in accordance with the above-described
procedure, to find the space distribution of the ioniza-
tion, detachment, attachment, etc. coefficients which en-
ter into the set of continuity equations for the main
charged components. At our experimental conditions,
we can restrict ourselves to the equations for electrons,
negative ozone ions ( −
3O ) and positive oxygen ions (
+
2O ), the concentrations of which considerably exceed
the concentrations of other ions. In our case of rather
low concentrations of water vapor (no more than 1%),
the −OH concentration, as indicated by the calculations
of the local chemical kinetics, does not approach −
3O ,
and therefore, we calculate only three mentioned kinds
of charged particles. Note that the electron concentra-
tion is often several orders of magnitude lower than the
ion concentrations, yet, owing to a high mobility of
electrons and large cross sections for the processes in-
volving electrons, the equation for electrons is major in
the set.
Results and discussions
The numerical simulation results give the character-
istic spatial distribution of the electric field strength and
charged particle concentration profiles as functions of
the distance from the needle-type electrode at different
voltages applied to the discharge gap. Among reactive
particles, of most interest for our consideration is ozone
which is produced in the discharge as a result of oxygen
molecule dissociation. It is well known that for the de-
struction of ozone produced in the discharge two cat-
alytic cycles are of importance: one is associated with
nitrogen oxides, and the other - with hydrogen radicals.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
1012
1013
1014
1015
(E /N )
0
=73 Td , T=300KO
zo
ne
c
on
ce
nt
ra
tio
n
T im e, 10 -3 s
P= 1 atm
O
2
=20% , N
2
=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 2 atm
O2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 3 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 5 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
0,0 0,5 1,0 1,5 2,0 2,5 3,0
1013
1014
1015
E/N =73 T d
O
zo
ne
c
on
ce
nt
ra
tio
n
Tim e, 10 -3 s
P= 1 a tm
N 2= 80% , O2=20%
O 2=99,5% , H 2O =0,5%
N 2= 50% , O2=50%
P= 2 atm
N 2= 80% , O2=20%
O 2=99,5% , H 2O =0,5%
N 2= 50% , O2=50%
P= 3 atm
N
2
= 80% , O
2
=20%
O 2=99,5% , H 2O =0,5%
N
2
= 50% , O
2
=50%
P= 4 atm
N 2= 80% , O2=20%
O 2=99,5% , H 2O =0,5%
N 2= 50% , O2=50%
P= 5 atm
N 2= 80% , O2=20%
O 2=99,5% , H 2O =0,5%
N 2= 50% , O2=50%
Fig. 1. Ozone concentrations for gas mixtures of vari-
ous compositions at different pressures
The first cycle can play a significant role only at a great
energy contribution that was not attained in the calcula-
tions. The other can be the cause of the ozone destruc-
tion also at a rather great energy contribution and a high
content of water vapor.
The introduction of a small quantity of water vapor
may cause the ozone concentration to increase, because,
first of all, the discharge voltage increases at the same
current value. At a higher voltage, the rate of oxygen
molecule dissociation is higher, and this fact plays a
positive role for the efficiency of ozone generation. The
real ozone yield is the result of competition between
two effects: (i) voltage increase and (ii) the ozone
breakdown in the corresponding catalytic cycle. As it is
obvious, for our conditions the other aspect of the water
vapor effect (that leads to a decreased ozone concentra-
tion) becomes of greater importance at OH 2 concentra-
tion higher than 1%.
Below (see Fig.1) we give the time evolution of the
ozone concentration for various gas mixtures (dry and
humid air, combined mixtures) at different parameters
(pressure, initial reduced electric field values). The tem-
perature was chosen to be 300 K. For air with a 1% wa-
ter content, as the pressure rises from 1 atm. to 5 atm.,
the ozone concentration increases 22 times (see Fig. 1)
at a reduced electric field strength ≈NE 73 Td (1 Td =
10-17 V/cm2), i.e., an approximately square pressure de-
pendence of ozone concentration takes place, that can
be explained on the basis of the structure of basic reac-
tions, where ozone is synthesized.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
109
1010
1011
1012
(E /N )
0
=7 3Td, T=300K
N
O
c
on
ce
nt
ra
tio
n
Tim e, 10 -3 s
P= 1 atm
O2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 2 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 3 atm
O
2
=20% , N
2
=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 5 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
0,0 0,5 1,0 1,5 2,0 2,5 3,0
105
106
107
108
109
1010
1011
(E /N )
0
=7 3Td, T=300K
N
O
2 c
on
ce
nt
ra
tio
n
Tim e, 10 -3 s
P= 1 a tm
O2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 2 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 3 a tm
O
2
=20% , N
2
=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 5 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
Fig. 2. NO and 2NO concentrations for dry and humid
air at different pressures
In this case, the concentration of harmful xNO com-
pounds (see Fig. 2) is 2-3 orders of magnitude lower
than the ozone concentration. Therefore, no excess of
boundary-admissible concentrations of xNO can be
provided at rather high ozone concentrations. For the
gas mixture 5,0:5,99: 22 =OHO at a 5-fold rise in
pressure, the ozone concentration increases by a factor
of 15 at a voltage even slightly higher than the reduced
electric field. The temperature dependence of the ozone
concentration (see Fig. 3) obviously shows that this con-
centration increases with temperature lowering (corre-
sponding increase of neutral particle density in the gas
mixture). However, it should be noted that in this case
the specific efficiency remains nearly constant, i.e., the
use of cooling may appear expedient to create ozonizers
with a higher ozone concentration. We note that here we
did not take into account the consumption of energy for
cooling, that might be a significant part of the total pow-
er expended.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
1013
1014
1015
1016
(E /N )
0
=146Td, P=1 atm
O
zo
ne
c
on
ce
nt
ra
tio
n
T im e, 10 -3 s
T =1 00K
O2=20% , N 2=8 0%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 00K
O2=20% , N 2=8 0%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 50K
O
2
=20% , N
2
=8 0%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =4 00K
O2=20% , N 2=8 0%
O
2
=20% , N
2
=79% , H
2
O =1%
O2=99,5% , H 2O =0,5%
Fig. 3. Ozone concentration for various gas mixtures at
different temperatures
For dry air, with a five-fold rise in pressure the elec-
tron concentration increases 35 times (from 2⋅106 to 7⋅
107 cm-3), see Fig. 4. And at the same rise in pressure for
the mixture 5,0:5,99: 22 =OHO the increase in the
electron concentration does not exceed a factor of 6 (see
Fig. 4). As to the gas mixture 50:50: 22 =ON , here
the increase in the electron concentration does not ex-
ceed a factor of 3 at a five-fold rise in pressure. The
comparison of the obtained numerical results shows the
following trends: (i) the higher is the humidity, the low-
er is the discharge current at the same voltage, or a high-
er voltage is required to maintain the same current val-
ue; (ii) the total quantity of nitrogen oxides decreases
with a successive replacement of the basic sort of oxide,
i.e., ON 2 by NO ; (iii) the variations in the concentra-
tions and composition of hydrogen-containing particles
are comparatively small. At a higher humidity, the dis-
charge in air approaches the thermodynamically equilib-
rium discharge. At 2% of H2O and higher, it is OH that
becomes the main negative ion. It is of interest to note
that for 1% and 2% of OH 2 , the evolution of electron
concentrations is not monotone. Among the particles
produced in the discharge, the OH radicals are the
most reactive. It can be seen that their concentration
first increases, then reaches maximum and decreases.
However, the duration of the increase strongly depends
on the water vapor content. This behavior results in a
complicated dependence of the maximum −OH radical
concentrations on time and the water vapor content.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
0
1x107
2x107
3x107
4x107
5x107
6x107
7x107
8x107
9x107 (E /N )
0
=7 3Td , T=300K
El
ec
tro
n
c
on
ce
nt
ra
tio
n
T im e, 10 -3 s
P= 1 a tm
O 2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 2 a tm
O 2=20% , N 2=80%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 3 a tm
O
2
=20% , N
2
=80%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 a tm
O 2=20% , N 2=80%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 5 a tm
O 2=20% , N 2=80%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
0,0 0,5 1,0 1,5 2,0 2,5 3,0
106
107
108
(E /N )
0
=146Td, P=1 atm
E
le
ct
ro
n
c
on
ce
n
tra
tio
n
T im e, 10 -3 s
T =1 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 50K
O2=20% , N 2=80%
O
2
=20% , N
2
=79% , H
2
O =1%
O2=99,5% , H 2O =0,5%
T =4 00K
O
2
=20% , N
2
=80%
O2=20% , N 2=79% , H 2O =1%
O
2
=99,5% , H
2
O =0,5%
Fig. 4. Electron concentration for dry and humid air at
different pressures and temperatures
The electron energy dependence of the electron dis-
tribution function is a very illustrative characteristic of
the discharge (see Fig. 5).
0 1 2 3 4 5
0,0
0,1
0,2
0,3
0,4
0,5
D
is
tr
ib
ut
io
n
F
un
ct
io
n
E lectron Ene rgy , eV
H 2O-1% , E/N =70 T d
H2 O-1%, E /N =140 T d
H2 O-1%, E /N =350 T d
H 2O-0% , E/N =70 T d
H2 O-0%, E /N =140 T d
H2 O-0%, E /N =350 T d
H2 O-0.5% , E/N =70 T d
H2O -0.5%, E /N =140 T d
H2O -0.5%, E /N =350 T d
O 2-100% , E/N =70 T d
O 2-100%, E /N =140 T d
O 2-100%, E /N =350 T d
O 2-99.5% , H2 O-0.5% , E/N =70 T d
O 2-99.5%, H2O -0.5%, E /N =140 T d
O 2-99.5%, H2O -0.5%, E /N =350 T d
Fig. 5. Electron energy distribution functions for vari-
ous gas mixtures at different values of the initial re-
duced electric field NE
Thus, it can be seen that the distribution function
reaches the energy up to 5 - 6 eV with an increase in the
reduced electric field from ≈NE 62 Td up to 350 Td.
However, in this case, the behavior of the distribution
function very strongly depends on the gas mixture com-
position. In particular, for the 5,0:5,99: 22 =OHO
mixture the distribution function is nearly constant in a
wide energy range (up to 10 eV). This indicates that
there is no effective channel of energy loss by electrons
almost up to 10 eV.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
10 8
10 9
1010
1011 (E /N )
0
=146Td, P=1 atm
O
3- c
on
ce
n
tra
tio
n
T im e, 10-3 s
T =1 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =3 50K
O
2
=20% , N
2
=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O =0,5%
T =4 00K
O2=20% , N 2=80%
O
2
=20% , N
2
=79% , H
2
O =1%
O2=99,5% , H 2O =0,5%
0,0 0,5 1,0 1,5 2,0 2,5 3,0
109
1010
(E /N )
0
=7 3Td, T=300K
O
2
- c
on
ce
nt
ra
tio
n
Tim e, 10 -3 s
P= 1 atm
O
2
=20% , N
2
=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 2 atm
O2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 3 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 5 atm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
Fig. 6. Concentration of negative ions O3
− for various
gas mixtures at different temperatures and pressures
The phenomenon known but not explained in the lit-
erature, namely, the rise in the discharge ignition volt-
age with an increasing ozone concentration, can be
rather well accounted for relying on two facts: (i) the
ion current is 20 to 40 times higher than the electron
current, and (ii) as a result of a great cross section for at-
tachment, the −
3O ions are the basic ions, their concen-
tration is more than 3 orders of magnitude higher than
the concentration of electrons. Therefore, despite the
fact that the ozone concentration makes about a few
tenths of percent of the oxygen molecule concentration,
the both gases are electronegative; a high concentration
of −
3O ions (they are just responsible for the basic cur-
rent transfer in the discharge) exerts a cardinal effect on
the current-voltage characteristic of the discharge,
specifically, on the ignition voltage.
The role of negative −OH ions is very significant
even at a low water content in the gas mixture (see
Fig.7). These ions assist the decrease of electrons in the
discharge, take up a substantial portion of ion current
and lead to the formation of complex cluster ions.
To compare on Fig. 8 it is shown the concentrations
of OH neutrals in various gas mixtures (humid) at dif-
ferent pressures.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
0,0
5,0x108
1,0x109
1,5x109
2,0x109
2,5x109
3,0x109
3,5x109
4,0x109
4,5x109
5,0x109 (E /N )
0
=73 Td , T=300K
O
H
- c
on
ce
nt
ra
tio
n
T im e, 10 -3 s
P= 1 a tm
O2=20% , N 2=80%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 2 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 3 a tm
O
2
=20% , N
2
=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O
2
=20% ,N
2
=79% ,H
2
O =1%
P= 4 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
P= 5 a tm
O2=20% , N 2=80%
O2=20% ,N 2=79.5% ,H 2O =0.5%
O2=20% ,N 2=79% ,H 2O =1%
0,0 0,5 1,0 1,5 2,0 2,5 3,0
10 7
10 8
10 9
10 10
10 11
(E /N )
0
=146Td, P=1 atm
O
H
- c
on
ce
nt
ra
tio
n
T im e, 10-3 s
T =1 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O = 0, 5%
T =3 00K
O2=20% , N 2=80%
O
2
=20% , N
2
=79% , H
2
O =1%
O2=99,5% , H 2O = 0, 5%
T =3 50K
O
2
=20% , N
2
=80%
O2=20% , N 2=79% , H 2O =1%
O
2
=99,5% , H
2
O = 0, 5%
T =4 00K
O2=20% , N 2=80%
O2=20% , N 2=79% , H 2O =1%
O2=99,5% , H 2O = 0, 5%
Fig. 7. Concentration of negative OH − ions for vari-
ous gas mixtures at different pressures and tempera-
tures. The indicated marks for dry air can be neglected
0,0 0,5 1,0 1,5 2,0 2,5 3,0
1011
1012
1013
(E /N )
0
=7 3Td, T=300K
O
H
c
on
ce
nt
ra
tio
n
Time, 10 -3 s
P= 1 atm
O 2=99.5% , H 2O =0.5%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 2 atm
O 2=99.5% , H 2O =0.5%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 3 atm
O
2
=99.5% , H
2
O =0.5%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 4 atm
O 2=99.5% , H 2O =0.5%
O
2
=20% ,N
2
=79.5% ,H
2
O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
P= 5 atm
O 2=99.5% , H 2O =0.5%
O 2=20% ,N 2=79.5% ,H 2O =0.5%
O 2=20% ,N 2=79% ,H 2O =1%
Fig. 8. Concentration of OH neutrals in various gas
mixtures (humid) at different pressures
Conclusion
Relying on the undertaken numerical simulation we
have established that for humid air (with 1% water va-
por content) with pressure rising from 1 atm. to 5 atm.,
the ozone concentration increases by a factor of 22 for a
time of 2x10-3 s at a reduced electric field strength поля
≈NE 73 Td (1 Td = 10-17 V/cm2), i.e., an approximate-
ly square pressure dependence of the ozone concentra-
tion takes place, that can be explained on the basis of
the structure of basic reactions, where ozone is synthe-
sized. In this case, the concentration of harmful xNO
compounds is 2 or 3 orders of magnitude lower than the
ozone concentration; therefore, no excess of boundary-
admissible concentrations of xNO can be provided at
rather high ozone concentrations.
For dry air, with a five-fold rise in pressure the elec-
tron concentration increases 35 times (from 2⋅106 to 7⋅
107 cm-3). And at the same rise in pressure for the mix-
ture 5,0:5,99: 22 =OHO the increase in the electron
concentration does not exceed a factor of 6. As to the
gas mixture 50:50: 22 =ON , here the increase in the
electron concentration does not exceed a factor of 3 at a
five-fold rise in pressure.
The known fact of the rise in the discharge ignition
voltage with an increasing ozone concentration was pro-
posed to be treated relying on two facts: (i) the ion cur-
rent is 20 to 40 times higher than the electron current,
and (ii) as a result of a great cross section for attach-
ment, the −
3O ions are the basic ions, their concentra-
tion is more than 3 orders of magnitude higher than the
concentration of electrons. Therefore, despite the fact
that the ozone concentration makes about a few tenths
of percent of the oxygen molecule concentration, and
the both gases are electronegative, a high concentration
of −
3O ions (they are just responsible for the basic cur-
rent transfer in the discharge) exerts a cardinal effect on
the current-voltage characteristic of the discharge,
specifically, on the ignition voltage.
This work was support in part by Science and Tech-
nology Center in Ukraine on project # 1069.
References
1. R. Morrow // Phys. Rev. A. 1985, vol. 32, p.1799-
1806.
2. Yu.S. Akishev, N.N. Elkin, A.P. Napartovich
// Plasma Physics Reports. 1986, vol.12, p.1225-
1234.
3. Yu.S. Akishev, I.V. Kochetov, A.I. Loboyko,
A.P. Napartovich. // Plasma Phys. Reports. 2002,
vol. 28, p.1054-1064.
4. V.I. Golota, V.I. Karas', V.P. Mal'khanov,
I.F. Potapenko, O.N. Shulika. Proc.XXVIII Zvenig-
orod Conf. on Plasma Physics and CTF. Moscow,
abstracts, 2001. p.161.
5. V.I. Golota, V.I. Karas', V.P. Mal'khanov, I.F.
Potapenko, O.N.Shulika. Proc.XXIX Zvenigorod
Conf. on Plasma Physics and CTF. Moscow, ab-
stracts, 2002, p.164.
6. Ph.M. Morse, H. Feshbach. Methods of Theoretical
Physics. New York, Toronto, London, McGraw-
Hill Book Company, Inc. 1953. Part 2, p.886.
В результате теоретических исследований и численного моделирования представляем следующие выводы:
для влажного воздуха при увеличении давления от 1.0133⋅105 до 5.0665⋅105 Пa концентрация озона в течение
2·10-3 с становится выше в 22 раза. Этот факт мы объясняем структурой реакций, в которых производится
озон. В этом случае концентрации вредных xNO на 2-3 порядка ниже концентрации озона; (ii) показано, что
азот полезен для производства озона в разряде; (iii) Основываясь на составе ионов мы объясняем увеличе-
ние напряжения зажигания разряда при возрастании концентрации озона даже при низкой концентрации
озона сменой электронного тока ионным, причем основными являются отрицательные ионы −
3O .
В результаті теоретичних досліджень та чисельного моделювання ми представляємо такі висновки: для
вологого повітря при підвищенні тиску від 1.0133·105 до 5.0665·105 Пa концентрація озону впродовж 2·10-3 с
стає вищою в 22 рази. Цей факт ми пояснюємо структурою реакцій, в котрих отримується озон. В цьому
випадку концентрації шкідливих xNO на 2-3 порядки нижчі, ніж концентрація озону; (ii) показано, що азот
корисний для генерації озону в розряді; (iii) На основі складу іонів ми пояснюємо збільшення напруги
запалювання розряду при зростанні концентрації озону навіть при низькій концентрації озону заміною
електронного струму іонним, причому основними є негативні іони −
3O .
Results and discussions
References
|
| id | nasplib_isofts_kiev_ua-123456789-111173 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-25T20:53:32Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Karas', V.I. Golota, V.I. Mal'khanov, V.P. Potapenko, I.F. Shulika, O.N. 2017-01-08T17:02:09Z 2017-01-08T17:02:09Z 2003 Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production / V.I. Karas', V.I. Golota, V.P. Mal'khanov, I.F. Potapenko, O.N. Shulika // Вопросы атомной науки и техники. — 2003. — № 4. — С. 247-253. — Бібліогр.: 6 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111173 533.9 In this paper as a result of the theoretical studies and a numerical simulation we presented the following main conclusions: (i) for humid air at increasing pressure of 1.0133 10⁵ Pa until 5.0665 10⁵ Pa ozone concentrations during 2·10⁻³s become higher in 22 times. This fact we clear with structure of ozone-production reactions. In this case the harmful NOx concentrations are 2-3 order lower than ozone one; (ii) it is shown that nitrogen is useful to ozone production in the discharge; (iii) based on ion collection we cleared increasing ignition discharge voltage at growing ozone concentrations even with low ozone concentrations. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Газовый разряд, ППР и их применения Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production Article published earlier |
| spellingShingle | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production Karas', V.I. Golota, V.I. Mal'khanov, V.P. Potapenko, I.F. Shulika, O.N. Газовый разряд, ППР и их применения |
| title | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production |
| title_full | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production |
| title_fullStr | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production |
| title_full_unstemmed | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production |
| title_short | Theoretical study of the non-steady discharge at atmospheric pressure in PIN - plate system and its application for ozone production |
| title_sort | theoretical study of the non-steady discharge at atmospheric pressure in pin - plate system and its application for ozone production |
| topic | Газовый разряд, ППР и их применения |
| topic_facet | Газовый разряд, ППР и их применения |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111173 |
| work_keys_str_mv | AT karasvi theoreticalstudyofthenonsteadydischargeatatmosphericpressureinpinplatesystemanditsapplicationforozoneproduction AT golotavi theoreticalstudyofthenonsteadydischargeatatmosphericpressureinpinplatesystemanditsapplicationforozoneproduction AT malkhanovvp theoreticalstudyofthenonsteadydischargeatatmosphericpressureinpinplatesystemanditsapplicationforozoneproduction AT potapenkoif theoreticalstudyofthenonsteadydischargeatatmosphericpressureinpinplatesystemanditsapplicationforozoneproduction AT shulikaon theoreticalstudyofthenonsteadydischargeatatmosphericpressureinpinplatesystemanditsapplicationforozoneproduction |