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**The study of thermal processes in an electrode**
**submitted to an electric arc**

J. Devautour, J. Chabrerie, Ph. Testé

**To cite this version:**

J. Devautour, J. Chabrerie, Ph. Testé. The study of thermal processes in an electrode submitted to an electric arc. Journal de Physique III, EDP Sciences, 1993, 3 (6), pp.1157-1166. �10.1051/jp3:1993191�.

�jpa-00248989�

J. Phys. III France 3 (1993) l157-l166 _{JUNE} 1993, _{PAGE} l157

Classification Physics Abstracts

02.70 06.70E 44. lo 52.80M

The study of thermal processes in _{an} electrode submitted _{to} _{an}
electric _{arc}

J. Devautour (I), J. P. Chabrerie (2) and Ph. Test£ (3)

(~) L-G-E-P- & Comptoir Lyon-Alemand-Louyot, 8 _{rue} Portefoin, 75139 Paris, France
j2) Laboratoire de Gdnie Electrique de Paris. CNRS jtJRA 127), Ecole Supdrieure d'Electricitd,

Plateau du Moulon, 91192 Gif _{sur} Yvette, France

(~) LGEP & Electricitd de France Les Renardidres, 77250 Moret _{sur} Loing, France
(Received 4 June J992, revised 8 October J992, accepted 3 No>.ember J992)

Abstract. This article investigates the thermal phenomena that _{are} occurring in _{an} electrode
submitted to an electric _{arc} in air at atmospheric _{pressure.} Our purpose is _{to} get a better

understanding of the electrode erosion phenomena conceming vaporization _{or} liquid droplets
ejection. For that _{we} propose an original experimental ^{device} allowing the measurement of the

liquid and vapor quantities created under the _{arc} root. The principle of this device is based _{on} the

ejection of the liquid metal through centrifugal movement of the electrodes during ^{the} arc. Some

results _{are} given relatively to Ag, Cu and AgSn02 cathodes and anodes. Then _{we} present a

numerical modelling of the thermal phenomena induced in the electrode by the heat transferred

from the _{arc} root. We propose a method _{to} solve the difficulties related to this kind of,« free

boundary _{»} problems induced by the fact that the electrode material may undergo various phase
changes. Finally _{we} show how _{to} _{use} this numerical computation and the experimental results in

order _{to} estimate the power density input at a copper anode.

Introduction.

The generation of _{an} electric _{arc} between electrodes remains _{a} widespread means of

interrupting an altemative _{or} direct _{current.} In such _{a} process, electrode materials _{are}
submitted _{to} the intense surface heating of the _{arc} _{root} that brings _{a} huge _{power} density to it

and causes subsequent erosion _{:}

by vaporization _{;}

by liquid metal departure under the action of the different body or surface forces exerted

on the liquid pool _{;}
by micro-explosions.

The aim of this study is to get a better understanding of the themlal phenomena occurring in

an electrode. Indeed, before apprehending the complex ^{mechanisms} ^{that} govem erosion, it is

primordial to determine quantitatively the _{amount} of vapor and liquid created under the _{arc}

root. In _{a} first part ^{we'll} ^{describe} an experimental device that permits to measure them. In _{a}

second part a 2D thermal model will be presented ^{that} ^{allows} to calculate these quantities. As
phase changes may occur we propose an original solution of the corresponding ^{free} boundary

problem.

An experimental set up permitting to evaluate the vapor and liquid quantities created by an arc.

DESCRIPTION. Figure I and figure 2 are respectively giving _{a} mechanical and _{an} electrical
schemes of the experimental device.

Two electrodes @ _{are} fixed, _{a} distance d apart, ^{in} a cylindrical vessel @ _{along} _{a} radial
direction. This vessel is made of _{a} conducting cylinder and possesses a vertical shaft 3

,

fixed
at its bottom and electrically insulated from it by means of _{a} glass-epoxy piece @. Ball-

bearings 3 allow this vessel _{to} be rotated _{at} _{an} arbitrary angular frequency _{w} _{up} to
300 rad,s~ As _{we} can see in figure I, _{one} ^{of} the _{two} electrodes is fixed _{on} the shaft, the other

one is fixed _{on} the cylinder inner wall, and the _{arc} current is brought to the electrodes trough
liquid Hg sliding electrical _{contacts} @. It is possible to show that the aerodynamic ^{flow}

conditions that get ^{installed} ^{in} ^{the} rotating cylinder _{are} such that there is _{no} velocity of the air

relatively _{to} the electrodes. Moreover, it may be easily shown that the forces acting _{on} the

charged particles present ^{in} ^{the} plasma _{are} several order of magnitude _{greater} than the

centrifugal force. We indeed could observe that the plasma _{was} not disturbed _{even} when the

vessel _{was} rotated at the maximum frequency. For instance for _{a} _{same} _{arc} current pulse

I(t), _{one} obtains the _{same} _{arc} voltage drop V~(t) for

w =

0 and _{w}

=

300 rad.s~ ^{'}

I _{Electrodes}

~ @Cylindfical Vessel

@ ver6cal shaft

~

@ glass-epoxy piece

$Ball-bearings

@ Liquid metal

sliding contacts

i ARC @ Base Piece

m _{Copper}

.:.II"--

__

i1nsu1atingmatera1

~ .[@j'_

._',

@ Mercury

;=_.j[I.=,.[__:...

Fig. I. Scheme of the mechanical part ^{of} ^{the} experimental device.

The,electrical _{power} supply consists of three parts

a main circuit @ allows to feed the electrodes with _{a} quasi half~sinusoidal _{current} (with

N° 6 ARC-ELECTRODE INTERACTIONS l159

LW~21mH _{A}

$ $

transformer

Fig. 2. Scheme of the electrical part ^{of} ^{the} experimental setup.

a maximum intensity I~~~ ^{in} ^{the} range of loo to 3 000 amperes and _{a} time duration in the range
of I to 20 milliseconds)

an auxiliary circuit @ allows _{to} charge the storage capacitor ^{bank} _{up} to 300 volts
the last circuit 3 is _{a} trigger circuit. Since a fixed gap of _{a} few millimiters is kept

between electrodes, the _{arc} has _{to} be triggered with a high voltage pulse. One should note that
the secondary coil of the high voltage transformer _{must} also be able to carry the _{arc} _{current} of _{a}
few thousands amperes.

The operating cycle of the experience is controlled with _{a} microcomputer _{:} a great ^{number} ^{of}
successive _{arcs} _{are} necessary, in order _{to} get a mass loss greater ^{than} ^{the} ordinary precision of

our balance (10~^{~} g).

Principle of the experiment. It is based _{on} _{a} very simple principle _{:} the liquid metal created

by the _{arc} _{on} the surface of the

« inner _{»} electrode is submitted to _{a} radial acceleration
y =

Rw ^{~}(R is the distance to the axis of rotation). When the corresponding centrifugal force
becomes sufficient, the whole liquid metal is ejected, and _{so,} this experimental _{setup} allows _{us}
to get a direct measurement of the total liquid and vapor quantities by simply weighing the
electrodes after _{a} given number of _{arcs.} Moreover, _{we} _{can} _{assume} that the _{mass} transfer from
the outer electrode _{to} the inner _{one} is negligible due to the distance of 5 _{mm} between electrodes
and _{to} centrifugal force.

Results and interpretation.

COMPARISON OF ANODE AND CATHODE EROSION FOR VARIOUS CONTACT MATERIALS. We

have compared the erosion between _{an} anode and _{a} cathode made of _{two} kinds of materials _{:}
pure silver _{or} pure copper (OFHC) _{;}

pseudo-alloys AgMeO (Ag with MeO grains dispersed inside) such _{as} AgCdO _{or}
AgSnO~.

The various experimental conditions adopted to test these materials _{are} the following _{:}

the gap between anode and cathode is kept constant and equal to 5 _{mm} _{;}

the _{arc} current pulse delivered _{to} the electrodes is semi-sinusoidal with the following

characteristics _{:}

1= 5 _{ms}

I~~~ _{m} ^{400} ^{A} ; Arc duration _{m} 5 _{ms} I (t ). dt

m 1.4 C

i o

It is important to speciJj that the experimental _{mass} ^{losses} presented were always
measured for _{an} electrode (anode _{or} cathode) fixed in _{an} _{«} inner _{»} position (see Fig. 3).

Indeed, the

« outer » electrode may receive liquid metal droplets ejected from the

« inner _{»}
electrode surface, and then the measurement of the _{mass} loss for the

« outer _{»} electrode would

not have any meaning.

The results, presented in figure 4, correspond to the mass loss per arc i>ersus the acceleration

y, for the _{arc} _{current} pulse given above.

- ~-A~g«< - cw~~ Armi

. An~ccu;v« n ~wwcwv«

-, ~-Aasno~ -~ -OW~ Agsnc~

-.-An~Amo --owwAmo

lo .Amwosnoj _{+} ~aw~cusno~j

formation of liquid _{on} _{~}

°~ tile surface of _{contacts} fl

i j

, u :~ .

~i i _{~i}

:. ^{>}

~

~ .-

it _{o-i}

--t-~ ^{*}

outer

m _{,,}

ii ^{~}

~fi ^{#} ^{0.Ol}

<

ym ^{R}

~ i

o.ooi '

0 50o 1000 150o 2000 2500

Acceleration (ms.?)

Fig. ^{3.} Fig. 4.

Fig. ^{3.} An illustration of the principle ^{of} the measurement of liquid quantities.

Fig. ^{4.} Comparison of erosion for different _{contact} materials obtained with the experimental rotating
setup.

NB _{:} The _{mass} loss is averaged over 500 _{arcs.} We _{must} precise that these results present a

very small scattering and that they _{are} independent of the total number of _{arcs,} above _{a} few
hundreds _{ones.}

For pure metals such _{as} Ag or Cu, _{one} _{can} note a great ^{difference} ^{of} ^{the} ^{erosion} ^{rate} ^{for} a
same material between the anode and the cathode. For Ag, the anode is nearly 250 times _{more}
eroded than the cathode at the maximum value of _{y.} This result, ^{which} is quite _{new,} ^{is} _{very}
surprising and shows clearly that there certainly ^{exists} a great discrepancy between the heat
flux characteristics, applied _{to} the surface of the cathode relatively to the anode.

For the anode, _{we} also observe _{a} very clear saturation effect of the erosion rate above _{a}
critical value y~ of the acceleration. This result confirms the fact that, above y~, the whole

liquid metal leaves the surface of the electrode. Moreover, the numerical modelling, that will
be described in the next chapter, allowed _{us} _{to} verify that there exists only a little difference

N° 6 ARC-ELECTRODE INTERACTIONS l161

(30 §b maximum) between the liquid quantities calculated with each _{one} of the two following
assumptions

I) the liquid does not leave at all the surface of the electrode (no ejection forces acting _{on} the

pool)

it) ^{the} liquid is expulsed ^{from} the surface _{as} _{soon} _{as} created by the _{arc} _{root.}

This remark and the results of figure 4, permit to deduce that only a small proportion of the
melted _{zone} is ejected when the electrodes _{are} at rest.

Materials containing metallic oxides (AgSnO~, AgCdO, CUSnO~) present different erosion
characteristics _{:} the erosion is quasi similar for both anode and cathode. It takes place at an

intermediate level between the anode and the cathode rates of _{a} pure metal. We _{can} also _{note}
that the erosion _{rate} _{versus} _{y} does not present a saturation effect _{as} _{neat} _{as} the _{one} shown by

pure metals. This may indicate that, for AgMeO _{or} CUMeO, _{a} certain quantity of the liquid
phase can remain _{on} the electrode. In fact, the proportion of oxide (nearly 20 §b in vol.) _{may}

considerably increase the viscosity of the liquid and also improve its adhesion and wetting
properties at the solid-liquid interface. Such _{a} problem ^{is} being studied at present ^{time} at

LGEP.

These results _{are} primordial to help _{us} _{to} understand erosion mechanisms. If, for instance,

we consider the _{case} of A.C. switching device electrodes which are altematively anode _{or}
cathode, results of figure 4 (for _{w}

= o) lead to the conclusion that for the _{arc} current pulse used
in _{our} experiment, _{pure} Ag contacts will give rise _{to} _{a} similar _{or} _{even} lower erosion rate than

AgMeO _{ones.} Of _{course,} such _{an} assertion does not take into account other parameters like
electrical contact resistance _{or} static and dynamic welding properties of _{contacts.} If _{now} _{we} do

the sum of the total _{mass} loss for the anode and for the cathode _{as} _{a} function of

w, we may see that the _{mass} loss becomes greater ^{for} pure metals than for pseudo alloys as
w increases. Moreover, _{we} have observed that the _{mass} loss is essentially due _{to} the ejection of

liquid metal. So the preceding remark may explain why AgMeO _{are} _{more} interesting than pure
metals for _{more} _{severe} _{arc} _{current} conditions (for which forces due to the _{arc} itself _{:} Marangoni
effect _{or} Lorentz forces, will be able to eject a substantial quantity of liquid).

2D modelling of thermal processes occurring in _{an} electrode.

DESCRIPTION OF THE MODEL. It would be quite interesting to _{see} whether the preceeding

measurements allow _{to} _{access} to a good order of magnitude of the power flux transferred by the

arc to the electrode. For that _{we} have elaborated _{a} thermal 2D computer ^{code.}

First of all _{we} have to recall _{some} results conceming the _{arc} itself

a high speed 16 _{mm} (5 000fps) laser cinematography [ii showed that, in air _{at}

atmospheric pressure, ^{the} cathodic _{arc} _{root} _{as} well _{as} the anodic _{one} _{are} working in _{a}
concentrated single spot regime and have _{a} circular shape

due _{to} the huge _{power} flux present ^{in} ^{the} arc root (lo~ _{to} 5 _{x} lo'°W/m~), the

temperature ^{of} ^{the} ^{material} ^{will} ^{increase} ^{and} ^{reach} ^{fusion} ^{and} vaporization temperature. So,

this thermal flux transfer problem is _{a} typical ^{ablation} problem that involves moving

boundaries.

Taking into account the above considerations, _{we} have adopted the following assumptions

for the modelling of the thermal phenomena occurring in _{an} electrode submitted _{to} _{an} electric

arc

I) _{an} axisymetric _{geometry} (see Fig. 5) is used

it) a given _{power} density Q(r, t) enters the upper surface of the electrode at its center ;

iii) the electrodes _{are} made of _{a} pure metal for which _{we} take into account the various phase
changes _{;}

Anodic

or

catllodic

R r

.-~

"'': 3T

~

' .~ . ... in ^{~}

T-To z

Fig. 5. The model of _{arc} heat transfer _{to} _{an} electrode adopted in the numerical simulation.

iv) the material is characterized by its constant density _{p} (no thermal dilatation) and also by

its specific heat capacity C~(T) and its thermal conductivity k(T), which will be taken both

dependent _{on} the temperature ^{T} ;

v) the liquid metal created _{on} the surface remains at _{rest} (no thermoconvection) _{;}
vi) the choosen boundary conditions _{are} _{:}

no heat flux _{on} the lateral sides of the electrode _{;}
T

= To ^{fixed} on the lower _{cross} section of the electrode.

Mathematical formulation of the problem. The unstationary equation of heat diffusion has
to be solved in the various phases (solid and liquid), after suppression of the terms of
thermoconvection and viscous dissipation. Moreover, heat balance equations _{across} phase
boundaries (solid-liquid and liquid-vapor) have also to be taken into account.

Our approach consisted in the _{use} of _{an} enthalpy function H(T) permitting to replace this

complicated set of equations by _{a} much simpler _{one} that may be written

p

I

=

div (K(T). VT) _{+} _{S}

S is _{a} body _{source} term (such as Joule Effect).

A piecewise linearization (see Fig. 6) allowed _{us} _{to} _{suppress} _{the} discontinuities of
H function for fusion _{or} vaporization.

Such _{a} method has already been described by several authors [2]. It permits _{to} avoid taking

into _{account} the location of phase change boundaries at each time step ^{of} the calculation of the

temperature field T(r, _{z,} t). These boundaries may be determined only ^{after} the calculation of
T has been achieved. It is, of _{course,} necessary ^{to} verify that the result does not depend _{on} the

temperature ^{interval} T~ Ti (see Fig. 6).

N° 6 ARC-ELECTRODE INTERACTIONS 1163

H

L

T~T~T, _{~}

Fig. 6. Linearization of the enthalpy function H(T).

The problem ofablation. As soon as vaporization _{occurs,} the surface _{on} which the heat flux
is applied does _{not} remain the _{same.} In order _{to} solve the numerical difficulties related to this
particular moving boundary, we propose an original method that consists in replacing the

vaporized zone with _{a} fictitious _{one} (see Fig. 7) that shall be govemed by the following
equation _{:} d~T/dz~

=

0 and in applying _{a} fictitious power flux Q~(r, t on the upper surface of
the grid. The physical imposed _{power} flux that _{we} wish _{to} apply _{on} the liquid-vapor ^{interface} ^{is}
Q(s, t), where _{s} is the curvilinear coordinate. So, _{as} _{soon} _{as} vaporization _{occurs,} a correction

has to be made (at each time step) in order to determine Qs (r, t) allowing to ensure the desired value of QIs, t).

The Kirchhoflf transformation. It is important to note that, for metals like Ag _{or} Cu, the

conductivity in the liquid is _{very} different from that in the solid state.

~~'~~

VAPOR

=0

z

Fig. 7. Modelling of vapor ablation.

The well-known Kirchhoff transformation [3] allows, by a simple ^{coordinate} change to take
these variations of thermal conductivity into _{account.}

Numerical _{treatment} of the equations. We used _{a} finite difference method and the equations

were numerized by using _{an} implicit scheme of discretization. Then a linear system ^{of}

equations was obtained and solved with _{a} SOR (Successive Over Relaxation) type algorithm.

The validation of this computer ^{code} was made with analytical _{or} numerical results issued
from literature.

Now, _{we} shall present ^{the} ^{influence} ^{of the} power density distribution Q(s, _{t}) on the liquid _{or}

vapor quantities. For that, a fixed power P and _{two} uniform power densities Qi and

Q~ were considered. In figures 8a and 8b, _{we} give for _{a} 8 _{mm} diameter copper electrode, the
calculation results in _{two} _{cases}

p _{=} 5 000 W and Q

= 2 _{x} 10~ W/m~, _{the} isotherms being given at time t

= 1.5 ms.

p

=

5 coo W and Q

=

2 _{x} lo W/m~, _{the} _{isotherms} being given at a much shorter time

t _{=} 40 _{~Ls.}

NE _{:} In the graphs presented ^{in} figures 8a and 8b, the heat source is applied at the lower left

hand _{comer} (points I to 20).

We _{note} that in the first _{case,} for _{a} stagnation time of 1.5 _{ms} _{no} metal has been vaporized,
whereas in the second _{case,} _{a} rather deep and _{narrow} hole has been made after _{a} much smaller

stagnation time.

Those examples of calculation show very clearly the influence that the power density _{may}

have _{on} phase changes.

Heat flux

~~~~~~ ~~~~~

04 4 420 40 5o 0 lo 20 30 40 50

X 47~tm X 4,7gm

= 1083 °C

fluX

## fl

40

Z _{X} 16gm Z X 16~m

~~j Solid Phase §~3Llquld _{Phase} ~J _{Vapor} _{Phase}

Isotherms for t~ = 1,5 _{ms} ^{Isotherms} for ts _{=} _{40 ~S}

P = 5000 W Q

= 2 109 W/m2 p _{=} 5000 W Q _{=} 2 1011 W/m2

a) b)

Fig. 8. a) Isotherms at time t _{=} 1.5 _{ms} for P

= 5 000 W, Qi

=

2 x10~ W/m~. Material is pure
copper. b) Isotherms at time _{t}

=

40 _{ms} for P

= 5 000 W, Q2 _{=} ^{2} x 10~' W/m~. Material is pure copper.