NUMERICAL SIMULATION OF A DECAYING ARGON ARC

(1)

HAL Id: jpa-00219088

https://hal.archives-ouvertes.fr/jpa-00219088

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

NUMERICAL SIMULATION OF A DECAYING ARGON ARC

T. Bracke, H. Sommer, C. Stojanoff

To cite this version:

T. Bracke, H. Sommer, C. Stojanoff. NUMERICAL SIMULATION OF A DECAYING ARGON ARC. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-239-C7-240. �10.1051/jphyscol:19797117�.

�jpa-00219088�

(2)

JOURNAL DE PHYSIQUE CoZZoque C7, suppZBment au n07, Tofie 40, ~ u i Z Z e t 1979, page C7- 239

NUMERICAL SIMULATION W A DECAYING ARGON ARC

T. Bracke, H.T. Sornmer and C.G. Stojanoff.

I n s ti t u t fiir Teehnische Thmnodynamik, R. W. T . H.

The arc parameters of an electric arc that is subjected to rapid temporal changes of the arc current, experience temporal and spatial variations due to the effects of reaction kinetics, conduction, convection, diffusion,viscous dissipation and radiation.

The purpose of this report is to present in concise form the results of the numeric- al simulation of a decaying,free burning, infinitely long, axissymmetric, laminar argon arc colw,n. The current interruption is idealized as a step function in time and the thermodynamic properties of the plasma are described by a mode1,which assumes local thermodynamic equilibrium and quasi-neutrality. The transport coeff.

are obtained from measurements performed on a free burning arc /5/ and from kinetic calculations /3,6/. The resulting system of equations consists of the momentum (I), energy ,(2) and continuity (5) equations and of the conservation equation for the atoms

(6) and the thermal equation of state (7) .

This set of equations is supplemented with the heat flow equation (31, the particle current density equation (4) and the mass fraction definitions (8) .

The dependent variables v,q , ^{T, p and} Yi

are functions of radius and time only. An implicit finite difference method is used which has an efficient time step control

Aachen, 51 00 Aaehen, W. Germany.

and the grid follows the developing radial solution.

+ f v &

av = - & a+ + r l [ L & q - 2 ~ ^{3 %} + F ^{J p}

^{1 4 1}

p = g R (2) ~ ; = ( 8 )

wi in equation (2) is the chemical source. 9 The system, of eq6ations 11-8) is solved using appropriate boundary and initial con- ditions /I/. The chemical source terms are specified by the following reactions

The corresponding rate coefficients are taken from the literature /2, 4, 7/. The dominant diffusion processes are the inward diffusion of atoms and the outward ambipol- ar diffusion of charged particles.

The results of the calculations for 60 psec after current interruption are presented

in Fig. 1 - ^{Fig. 5.}

17

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797117

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The percentage of ionization drops from 6 % to 4 % after 60 rsec and goes down to 2.5 % after 200 psec. These results are con- sistent with data on the decay of the elec- trical conductivity. The temperature decay is linear in time and depends strongly upon the chemical reactions involved. Moreover, the present numerical analysis shows a very complex behaviour of the nonstationary arc with wave motion in the arc column starting immediately after current inter- ruption.

References:

/1/ Kollmann, W., Sommer, H.T., Stojanoff, C.G.: J. Non-Equilib. Thermodyn. Vo1.2

1977

/2/ Uhlenbusch, J., Fischer, E., Hackmann, J.: Bericht HMP 128, 1975

/3/ Hirschfelder, Curtiss, Bird, John Wiley 1967

/4/ Bond, J.W., Phys. Rev., Vol. 105, NO. 6, 1957

/5/ Stojanoff, C.G., Jahrbuch DGLR, 1971 /6/ McDaniel, E.W. John Wiley, 1964 /7/ Hoffert, M. Phys. of Fluids, Vol.11,

NO. 1, 1968

6 10

RADIUS l M M l

Fig.1 Radial Profiles of.Degree of Ionisation

0 1 2 3

RADIUS lUU l

Fig.2 Radial Temperatureprofiles

Fig.3 Radial Velocityprofiles

Fig.4 Radial Pressureprofiles

I

0 20 &O

w

80 I r n

TIME I LS I

NUMERICAL SIMULATION OF A DECAYING ARGON ARC

HAL Id: jpa-00219088

https://hal.archives-ouvertes.fr/jpa-00219088

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

NUMERICAL SIMULATION OF A DECAYING ARGON ARC

T. Bracke, H. Sommer, C. Stojanoff

To cite this version:

T. Bracke, H. Sommer, C. Stojanoff. NUMERICAL SIMULATION OF A DECAYING ARGON ARC. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-239-C7-240. �10.1051/jphyscol:19797117�.

�jpa-00219088�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZBment au n07, Tofie 40, ~ u i Z Z e t 1979, page C7- 239

NUMERICAL SIMULATION W A DECAYING ARGON ARC

T. Bracke, H.T. Sornmer and C.G. Stojanoff.

I n s ti t u t fiir Teehnische Thmnodynamik, R. W. T . H.

The arc parameters of an electric arc that is subjected to rapid temporal changes of the arc current, experience temporal and spatial variations due to the effects of reaction kinetics, conduction, convection, diffusion,viscous dissipation and radiation.

are obtained from measurements performed on a free burning arc /5/ and from kinetic calculations /3,6/. The resulting system of equations consists of the momentum (I), energy ,(2) and continuity (5) equations and of the conservation equation for the atoms

(6) and the thermal equation of state (7) .

This set of equations is supplemented with the heat flow equation (31, the particle current density equation (4) and the mass fraction definitions (8) .

The dependent variables v,q , T, p and Yi

are functions of radius and time only. An implicit finite difference method is used which has an efficient time step control

Aachen, 51 00 Aaehen, W. Germany.

and the grid follows the developing radial solution.

av = - & a+ + r l [ L & q - 2 ~ 3 % + F J p

p = g R (2) ~ ; = ( 8 )

wi in equation (2) is the chemical source. 9 The system, of eq6ations 11-8) is solved using appropriate boundary and initial con- ditions /I/. The chemical source terms are specified by the following reactions

The corresponding rate coefficients are taken from the literature /2, 4, 7/. The dominant diffusion processes are the inward diffusion of atoms and the outward ambipol- ar diffusion of charged particles.

The results of the calculations for 60 psec after current interruption are presented

in Fig. 1 - Fig. 5.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797117

References:

/1/ Kollmann, W., Sommer, H.T., Stojanoff, C.G.: J. Non-Equilib. Thermodyn. Vo1.2

1977

/2/ Uhlenbusch, J., Fischer, E., Hackmann, J.: Bericht HMP 128, 1975

/3/ Hirschfelder, Curtiss, Bird, John Wiley 1967

/4/ Bond, J.W., Phys. Rev., Vol. 105, NO. 6, 1957

/5/ Stojanoff, C.G., Jahrbuch DGLR, 1971 /6/ McDaniel, E.W. John Wiley, 1964 /7/ Hoffert, M. Phys. of Fluids, Vol.11,

NO. 1, 1968

Fig.1 Radial Profiles of.Degree of Ionisation

Fig.2 Radial Temperatureprofiles

Fig.3 Radial Velocityprofiles

Fig.4 Radial Pressureprofiles

w

Fig.5 Decay of axial Temperature

The dependent variables v,q , ^{T, p and} Yi

av = - & a+ + r l [ L & q - 2 ~ ^{3 %} + F ^{J p}

in Fig. 1 - ^{Fig. 5.}