The transport of the erosion products of electrodes in electric arcs
Electrodes vapour material transport characteristics in the free-burning electric arc and formation of its pressure gradients are investigated. It is shown that adequate defining of gas-dynamic characteristic of electric arc plasma demands successive account of the thermal conductivity processes in...
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| Zitieren: | The transport of the erosion products of electrodes in electric arcs / V.A. Zhovtyansky // Вопросы атомной науки и техники. — 2003. — № 1. — С. 140-143. — Бібліогр.: 9 назв. — англ. |
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| citation_txt | The transport of the erosion products of electrodes in electric arcs / V.A. Zhovtyansky // Вопросы атомной науки и техники. — 2003. — № 1. — С. 140-143. — Бібліогр.: 9 назв. — англ. |
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| description | Electrodes vapour material transport characteristics in the free-burning electric arc and formation of its pressure gradients are investigated. It is shown that adequate defining of gas-dynamic characteristic of electric arc plasma demands successive account of the thermal conductivity processes in the channel arc region. The roles of the gas-dynamic and diffusion processes as transfer mechanisms of electrodes erosion products are compared. The method using distant stabilized wall to study the transfer processes out of channel proposed.
Досліджуються особливості поширення пари електродного матеріалу у відкритій електричній дузі та формування обумовлених нею градієнтів тиску. Показано, що адекватне визначення газодинамічних властивостей електродугової плазми вимагає послідовного урахування процесів теплопровідності в приканаловій області дуги. Порівнюється роль газодинамічних і дифузійних процесів як механізмів відведення продуктів ерозії електродів. Запропонований метод теоретичних досліджень процесів перенесення з використанням віддаленої від каналу дуги стабілізуючої квазі-стінки.
Исследуются особенности распространения паров электродного материала в открытой электрической дуге и формирования обусловленных ими градиентов давления. Показано, что адекватное определение газодинамических свойств электродуговой плазмы требует последовательного учета процессов теплопроводности в приканальной области дуги. Сравнивается роль газодинамических и диффузионных процессов как механизмов отведения продуктов эрозии электродов. Предложен метод теоретических исследований процессов переноса с использованием удаленной от канала дуги стабилизирующей квази-стенки.
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THE TRANSPORT OF THE EROSION PRODUCTS OF ELECTRODES IN
ELECTRIC ARCS
V.A. Zhovtyansky
Radiophysics Department, Taras Shevchenko Kiev National University, Ukraine
Electrodes vapour material transport characteristics in the free-burning electric arc and formation of its pressure
gradients are investigated. It is shown that adequate defining of gas-dynamic characteristic of electric arc plasma
demands successive account of the thermal conductivity processes in the channel arc region. The roles of the gas-
dynamic and diffusion processes as transfer mechanisms of electrodes erosion products are compared. The method
using distant stabilized wall to study the transfer processes out of channel proposed.
PACS: 52.80.-s
1. INTRODUCTION
Comparing with other forms of gas discharge the
electric arc is characterized with minimum loses of
energy on the transport of electricity within it’s channel.
This property designates the wide application of electric
arc plasma in modern high-technologies. Particularly it
concerns the electric arcs, free-burning between melting
electrodes in gas atmosphere, where the properties of
plasma in arc channel are defined by metal vapours
resulted from the products of electrodes erosion. Gas
atmosphere, where the electrodes are located, represent
practically inert component of plasma, because the
ionization potential of metal atoms is, as a rule, smaller
than the gas one [1]. Further the metal vapours, coming
through neutralization processes, diffuse into the ambient
space.
In numerous investigations of free-burning arcs
between melting electrodes in the gas atmosphere at some
pressure p∞ (as a rule p∞=1 atm) the pressure a priori is
considered to be constant along the arc radius r, both in
the arc channel and outside: p(r)= p∞=const. The validity
of such assumption from the view point of the dynamics
of originated stream of metal vapours is analyzed below.
2. THE TRANSFER PROCESSES IN THE
ELECTRIC ARCS
The electric arc of approximately cylindrical shape,
initiated between flat faceplate melting electrodes with
small inter electrode distance, is investigated. As the
plasma properties almost exclusively defined by metal
vapours [1, 2], it is possible in the first approximation to
consider the most general dynamic properties of erosion
product flows on the example of it transport into their
own atmosphere.
The essential feature of concerned system is principal
absence of the solution for the transport equations
(diffusion and thermal conductivity) for cylindrical type
of arc [2,3]. At the level of the general properties of
electric arc the unstable regime of burning of long arc
discharges corresponds to this state. Truly, as a result of
single integration of expression for thermal flux density ω
for cylindrical source
ω=-2πrλ⋅ (dT/dr) =-2πr⋅(dS/dr) (1)
(where λ – thermal conductivity coefficient, T –
temperature, ∫=
T
dTTS
0
)(λ – thermal potential) in the
region from the arc channel R to r>R the value of thermal
flux Q from unit of length can be obtained. It equals:
Q=2πr[S(R)-S(r)]/ln(r/R). (2)
So if r→∞ then Q→0, so the thermal flux, which can be
transferred due to the thermal conductivity from
cylindrical source decreases to zero logarithmically. The
same feature is characteristic for the diffusion processes.
This limitation vanishes for the spherical source: here
because of influence of geometrical factor the gradients
are sufficient to provide the corresponding transport
processes. It is especially essential, that for distances from
axis r>L of any electric arc, where L – its length, the
problem becomes spherically symmetrical. So there is no
sense to consider the problem in cylindrical geometry for
r→∞ (more precisely when r>L). At the same time the
problem for spherical source is independently interesting
related to formation of erosion products stream on the
electrodes surface (electrode spots). Here the inflow of
electrodes material vapour into the arc channel takes a
place practically in the point source regime and has a
character, close to hemispherical flow.
In the strict sense due to the influence of thermal
conductivity processes the arc often shapes near to
ellipsoidal, especially in so-called short and transition
types of arcs [3]. In this aspect it is possibly to consider
cylindrical and spherical sources as a extreme cases of
real source existence.
In practice the problem of unstable functioning of
electric arc is solved often by application of so-called
stabilized walls where the surplus thermal and diffusion
fluxes are “freezing”. Ordinary they are in contact with
electric arc plasma. In the experiments [1, 2], where the
stabilized wall was absent physically, their role actually
plays convection, which take off mention thermal and
diffusion fluxes, initialized in the arc channel.
3. THE DYNAMIC OF ELECTRODES
EROSION PRODUCTS
In contrast to transfer process the gas-dynamic
problem for the ideal gas flow from a cylindrical source,
as in the case of spherical one, has a solution [4]. In this
connection the considered here problem of gas-dynamic
process investigation has independent interest with
relation to study the qualitative influence arising here
flow on the general electric arc properties.
It is supposed that the arc channel is a cylindrical
source of electrodes material products. The distribution of
mass production rate per unit volume is uniform. It is
140 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 140-143
because of the influence of electromagnetic forces on
plasma stream at the near electrodes region, where the
plasma jet of erosion material take place along the axis of
arc (see [5]). Moreover in the arc area the velocity of gas
propagation is maximum because of the maximum value
of temperature T; it describes by sound velocity
a=(γR0T/µ)1/2 (3)
(where R0 – universal gas constant, γ – ratio of specific
heats, µ – molecular weigh of gas). The mechanism of
diffusion transfer of metal vapour is the most essential in
the arc channel too [3]. The consumption of initial
concentration of erosion products in the arc channel
corresponds to the upper value of pressure drop on its
boundary.
In such form the problem corresponds to channel
model of electric arc [6]. In order to obtain the dynamic
characteristics of the radial flow of electrodes material
erosion products the system of gas dynamics equation
was solved in isothermal approximations for the arc
channel (mass source) and in the adiabatic approximation
for the outside regions.
The continuity equation for the stationary flow is:
ρq=(r/R)Q/υπRυL2-υ, r≤R;
ρq=Q/υπRυL2-υ, r≥R.
(4a)
(4b)
Here ρ – density, q – the local flux velocity, υ –
geometrical factor, which is: υ=1 for the cylindrical
geometry and υ=2 for the spherical one, R – radius of
mass source. In the case of cylindrical source R
corresponds to the arc radius, and L – to the inter
electrode separation. The erosion rate for mass source is
Q=kI, (5)
where I – arc current, k – sputtering coefficient, which for
the cooper electrodes can reach the value 10-5 g/Cl [7]. It
is considered that the cathode spot fills with erosion
product half-sphere (for υ=2) or cylinder of length L/2
(for υ=1). The equations (4) are correct independently on
assumption of isothermal flow.
To obtain the flow parameters the motion equation is
used:
ρqdq=-dp, (6)
where ρ and q are connected by state equation
p=ρR0T(1+α)/µ; (7)
here α – is a degree of plasma ionization. For the arcs in
the metal vapour
α<<1. (8)
Taking into account that according to the channel model
[6] the regime is isothermal
T(r)=T0=const, (9)
as a result of single integration the solution of motion
equation for source region is obtained
(qR
2-q2)/2=R0T0/µ⋅ ln(p/pR), (10)
where the arc parameters on the channel boundary (where
r=R) are marked by index “R”. Next using the state
equation (7), the continuity equation (4a) for υ=1 and the
equation (3) and (8) follows the flow character in the arc
region in an explicit form:
R
rMM
M
M
TR
qq
q
q R
R
RR
R
=
−=
−
2
exp
2
exp
22
00
2
µ
(11)
Here the Mach number is entered
M=q/a. (12)
The solution for ρ0/ρR it is possible to find by
substitution (11) into (4a):
ρ0/ρR=exp(MR
2/2) (13)
where the parameter on the arc axis is marked by index
“0”. Moreover, according to (4a)
qR=Q/(πRLρR). (14)
It is not difficult to check on that the solution (11)
becomes ambiguous on the source boundary r=R if
MR>1. It means that here there is the parameters
discontinuity – the shock wave (SW) [4]. At the same
time the solutions (13) and (14) include the relationship
on its front automatically.
The estimations for the typical value of current,
corresponding to the SW mode, on the example of free-
burning electric arc between cooper electrodes of small
radius (R=1 mm) with the length L=3 mm were made. For
the typical values of MR=1 and, correspondingly,
qR=q=a0, and for the typical temperature T0=104 K, from
the expression (4) and (5) follows:
I*=πRLρa0/k≈7⋅104 A (15)
Thus, for the typical arc currents I~102 A in welding arcs
the subsonic regime of erosion products flow is realized.
Concerning the region of arc’s “root” at the
electrode’s surface define interest has a solution of the
same problem for the spherical source. For υ=2 in (4) we
find the typical radius R* of region, where the intense
metal inflow into the electrodes gap takes place:
R*=kI/(2πRρa0)1/2 or
R*(mm)=(0.35-0.45)⋅[I(A)]1/2.
(16)
The parameters range in the last expression corresponds
to the limit values of cooper content in atmospheric air for
arc channel from 0 % to 100 %. This range takes into
account the dependence ρ~µ and a0=(γ /µ)1/2, where γ=5/3
and µ=63.5 for cooper and γ=7/5 and µ=24 for nitrogen
molecules as main component of air.
Thus for the typical values of discharge currents the
values R* is about 1 mm, what is in good agreement with
the observed in experiments the radius of intense
luminous ball near the electrodes [2].
Concerning the flow dynamic in adiabatic
approximation regime for the regions outside of source
(e.g. arc channel) the following expression is typical:
p/pR=(ρ/ρR)γ. (17)
It is necessary to underline that adiabatic regime of
flow for the arc outside regions is nonrealistic. Really, the
experimentally observed temperature ratio is T0/T∞~30.
141
Thus the following ratio of pressure must correspond to
this temperatures:
p0/p∞=(T0/T∞)γ/(γ-1)=305/2 (18)
So in the role of agent, who can provide the transfer of
thermal energy from every partial unit of erosion products
in adiabatic expansion might be the pressure, whose
heavy gradient in this case can provide the mass- and heat
transfer from arc channel. However such drop isn’t
natural for the real arcs between melting electrodes in gas
atmosphere [1].
In reality another regime is realized: the influence of
thermal conductivity prevail in the high temperature
region near the arc channel and it solves the problem of
thermal transfer. This is like to pulse plasma processes,
where SW are replaced often by heat-wave as very
effective mechanism to equalize the heavy pressure
gradients [2].
4. THE COMPARISON OF THE ROLES OF
GAS-DYNAMIC AND DIFFUSION
PROCESSES
In the last paragraphs instead of real mixtures of metal
vapour (including it’s ionized components) and ambient
gas, the some effective gas medium with аveraged
molecular weigh µ of it’s components is considered
µ=∑i xiµi, (19)
where
xi=ni/n – (20)
the content of single component with the density ni in the
mixture with the total density n.
However gas-dynamic approach gives no way of
deducing the contribution of effects, connected with
mixture separation. Really, in electric arc with melting
electrodes the diffusion flux to the periphery regions also
takes a place [8].
In the general case to the arbitrary mixture of gas and
metal vapour it is possible to summarize, that as a result
of joint action of gas-dynamic and diffusion processes on
the arc boundary the total transfer of metal vapour
through unit square to the arc periphery is
Jm=xmJG+Jm
D=Q/πRL, (21)
where according to (14)
JG=qRρR, (22)
and the Jm
D finds according to [8].
In one's turn in the mixture the gradient of gas content
xg=1-xm determines so that in the conditions of opposite
diffusion flux of metal vapour and gas-dynamic flow of
mixture as a whole in the laboratory co-ordinates the
directed motion of gas component absent. This means that
the following expression is corrected:
xgJG
=(1-xm)JG =Jg
D. (23)
Here the subscripts m and g refer to metal vapour and gas,
correspondingly.
Depend upon the effectiveness of gas-dynamic and
diffusive mechanisms of electrode erosion products trans-
fer in the arc the metal vapour content is established,
which can be estimated according to (21)
xm
= 1- Jm
D/JG. (24)
As a rule in the channel of arc, free burning between
melting electrodes, the metal vapour content isn’t exceed
1 % [1-4]. This means that the influence of diffusion
processes is considerable.
The resume about exceeding influence of diffusion
processes is correct only for the arc channel. According to
the estimations (16) for the region of arc’s “root” on the
electrode surface as spherical source of erosion products
to the interelectrode space the gas-dynamic processes
exceed.
5. THE METHOD OF STABILIZING WALL
SEPARATED OF ELECTRIC ARC PLASMA
TO STUDY TRANSFER PROCESSES
To take into account nonadiabatic processes in real
electric arcs, the numerous calculation of the radial flow
of electrodes material erosion products was fulfilled. In
this case the radial profile of temperature was adopted
from experiment [1]. The result is that essentially the drop
of pressure takes place in the region of temperature
gradients. It does mean, that the main dynamic processes
are grouped nearby arc channel.
To exclude the role of convection, which depends on
arc position and has no regular influence on the arc
processes, the stabilized wall may be used. Contrary to
common electric arc devices, where the plasma is in
contact with this wall, in the proposed system the wall
should be offset by some distance from the arc.
To study the transfer processes out of channel region
this distance due to be satisfy some requirements. On the
one hand, the wall due to be on some distance ∆R away
from the channel, so the arc was free-burning and on the
other hand this distance should not be exceeded a limiting
position Rw
max where this wall still capable take off thermal
and diffusion fluxes, initialized in the arc channel.
The basic requirements are follows.
∆R >> lw, (25)
where lw is length of plasma wall layer which consist of
0.04 mm in electric arc argon plasma of atmospheric
pressure [9].
∆R > ld, lh, (26)
where ld and lh are diffusion and heat conductivity lengths.
R+∆R < Rw
max (27)
(see above).
R+∆R < L/2, (28)
where L is length of electric arc (see Sec. II).
Zone between arc channel and stabilizing wall in
theoretical treatment may include not only diffusion and
heat conductivity processes but also radiation transfer in
self-consistent mode.
Another way of looking at this problem is determining
Rw
ma dependly on electric arc plasma parameters. It may
be useful to study heat conductivity efficiency in electric
arc devices.
The obtained formulations can be used also for the
independent electrode material sputtering coefficient k
determining based on spectroscopic measurements of it
142
content in the arc channel (as it was made in [1, 4]) taking
into account the final dependence this content from the
source power Q according to (5). For this aim the special
arc device with determined geometry of the electrodes
and stabilized walls can be used. This will allow to
calculate the influence of transfer processes at most
accurately.
REFERENCES
1.I.L. Babich, A.N. Veklich, V.A .Zhovtyansky// Ukr.
Phys. J., 44 (1999) 963.
2.V.A. Zhovtyansky. Physical properties of dense low-
temperature nonuniform plasma: thesis for a Doctor of
Science degree (physics and mathematics): 01.04.08 -
plasma physics. Taras Shevchenko Kyiv National
University. Кyiv. 1999, p. 300.
3.V.A. Zhovtyansky, V.M. Patriyuk// Ukr. Phys. J., 45
2000, 1059.
4.G.G. Chorny. Dynamics of gases/ М:Nauka. 988, p.
424.
5.The physics of welding // Ed. by J. F. Lancaster. /
Oxford: Pergamon Press, 1984, р. 340.
6.Raizer Yu. P. Foundations of modern physics of
discharge processes/ М.: Nauka, 1980, p. 416.
7.Aksenov I. I., Khoroshich V. M. Participles flows and
mass transfer in the vacuum arc: review of dates of
native and foreign literature for the period 1931-1983
years./ Мoscow: CRIatominform, 1984, p. 54.
8.Zhovtyansky V.A., Murphy A.B., Patriyuk
V.M.//Problems of Science and Technology. Ser:
Plasma Physics. 2002, N 5(8), p.124.
9.Benilov M.S. //J. Phys. D: Appl. Phys. 28,1995, 286.
ПОШИРЕННЯ ПРОДУКТІВ ЕРОЗІЇ ЕЛЕКТРОДІВ В ЕЛЕКТРИЧНИХ ДУГАХ
В. А. Жовтянський
Досліджуються особливості поширення пари електродного матеріалу у відкритій електричній дузі та
формування обумовлених нею градієнтів тиску. Показано, що адекватне визначення газодинамічних
властивостей електродугової плазми вимагає послідовного урахування процесів теплопровідності в
приканаловій області дуги. Порівнюється роль газодинамічних і дифузійних процесів як механізмів відведення
продуктів ерозії електродів. Запропонований метод теоретичних досліджень процесів перенесення з
використанням віддаленої від каналу дуги стабілізуючої квазі-стінки.
РАПРОСТРАНЕНИЕ ПРОДУКТОВ ЭРОЗИИ ЭЛЕКТРОДОВ В ЭЛЕКТРИЧЕСКИХ ДУГАХ
В.А. Жовтянский
Исследуются особенности распространения паров электродного материала в открытой электрической дуге и
формирования обусловленных ими градиентов давления. Показано, что адекватное определение газодина-
мических свойств электродуговой плазмы требует последовательного учета процессов теплопроводности в
приканальной области дуги. Сравнивается роль газодинамических и диффузионных процессов как механизмов
отведения продуктов эрозии электродов. Предложен метод теоретических исследований процессов переноса с
использованием удаленной от канала дуги стабилизирующей квази-стенки.
143
references
|
| id | nasplib_isofts_kiev_ua-123456789-110616 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:25:33Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Zhovtyansky, V.A. 2017-01-05T18:57:35Z 2017-01-05T18:57:35Z 2003 The transport of the erosion products of electrodes in electric arcs / V.A. Zhovtyansky // Вопросы атомной науки и техники. — 2003. — № 1. — С. 140-143. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.80.-s https://nasplib.isofts.kiev.ua/handle/123456789/110616 Electrodes vapour material transport characteristics in the free-burning electric arc and formation of its pressure gradients are investigated. It is shown that adequate defining of gas-dynamic characteristic of electric arc plasma demands successive account of the thermal conductivity processes in the channel arc region. The roles of the gas-dynamic and diffusion processes as transfer mechanisms of electrodes erosion products are compared. The method using distant stabilized wall to study the transfer processes out of channel proposed. Досліджуються особливості поширення пари електродного матеріалу у відкритій електричній дузі та формування обумовлених нею градієнтів тиску. Показано, що адекватне визначення газодинамічних властивостей електродугової плазми вимагає послідовного урахування процесів теплопровідності в приканаловій області дуги. Порівнюється роль газодинамічних і дифузійних процесів як механізмів відведення продуктів ерозії електродів. Запропонований метод теоретичних досліджень процесів перенесення з використанням віддаленої від каналу дуги стабілізуючої квазі-стінки. Исследуются особенности распространения паров электродного материала в открытой электрической дуге и формирования обусловленных ими градиентов давления. Показано, что адекватное определение газодинамических свойств электродуговой плазмы требует последовательного учета процессов теплопроводности в приканальной области дуги. Сравнивается роль газодинамических и диффузионных процессов как механизмов отведения продуктов эрозии электродов. Предложен метод теоретических исследований процессов переноса с использованием удаленной от канала дуги стабилизирующей квази-стенки. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies The transport of the erosion products of electrodes in electric arcs Поширення продуктів ерозії електродів в електричних дугах Рапространение продуктов эрозии электродов в электрических дугах Article published earlier |
| spellingShingle | The transport of the erosion products of electrodes in electric arcs Zhovtyansky, V.A. Low temperature plasma and plasma technologies |
| title | The transport of the erosion products of electrodes in electric arcs |
| title_alt | Поширення продуктів ерозії електродів в електричних дугах Рапространение продуктов эрозии электродов в электрических дугах |
| title_full | The transport of the erosion products of electrodes in electric arcs |
| title_fullStr | The transport of the erosion products of electrodes in electric arcs |
| title_full_unstemmed | The transport of the erosion products of electrodes in electric arcs |
| title_short | The transport of the erosion products of electrodes in electric arcs |
| title_sort | transport of the erosion products of electrodes in electric arcs |
| topic | Low temperature plasma and plasma technologies |
| topic_facet | Low temperature plasma and plasma technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110616 |
| work_keys_str_mv | AT zhovtyanskyva thetransportoftheerosionproductsofelectrodesinelectricarcs AT zhovtyanskyva poširennâproduktíverozííelektrodívvelektričnihdugah AT zhovtyanskyva raprostranenieproduktovéroziiélektrodovvélektričeskihdugah AT zhovtyanskyva transportoftheerosionproductsofelectrodesinelectricarcs |