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Research Papers: Heat and Mass Transfer

Analytical Solution for the Electric Arc Dynamics and Heat Transfer When Exposed to a Magnetic Cross-Field

[+] Author and Article Information
Youssef Abdo

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et
Systèmes Énergétiques,
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France
e-mail: youssef.abdo@mines-paristech.fr

Vandad Rohani, François Cauneau

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et
Systèmes Énergétiques,
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France

Laurent Fulcheri

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et Systèmes
Énergétiques,
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 7, 2017; final manuscript received September 27, 2017; published online March 9, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(6), 062002 (Mar 09, 2018) (11 pages) Paper No: HT-17-1068; doi: 10.1115/1.4038602 History: Received February 07, 2017; Revised September 27, 2017

The motion of the gliding DC electric arc under the effect of magnetic field is investigated. The temperature distribution in the inside and the outside of the moving arc is computed. The temperature distribution for the fixed-spot arc is also obtained. It appears that the gas relative velocity inside the arc gives rise to heat convection, which has an impact on the arc motion. A practical analytical solution is derived using magneto gas dynamic equations in order to investigate the heat transfer occurring in the arc and its vicinity, to determine its characteristics, and to estimate its velocity when it is exposed to external and electrode-induced magnetic fields. Two methods are suggested: one for the free-burning arc and the other for arc burning between close surrounding walls.

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References

Maecker, H. H. , and Stablein, H. G. , 1986, “What Keeps an Arc Standing in a Cross Flow,” IEEE Trans. Plasma Sci., 14(4), pp. 291–299. [CrossRef]
Nemchinsky, V. , 2016, “Modeling Arc in Transverse Magnetic Field by Using Minimum Principle,” IEEE Trans. Plasma Sci., 44(11), pp. 2932–2935. [CrossRef]
Abdo, Y. , Rohani, V. , Cauneau, F. , and Fulcheri, L. , 2017, “New Perspectives on the Dynamics of AC and DC Plasma Arcs Exposed to Cross-Fields,” J. Phys. D: Appl. Phys., 50, p. 065203. [CrossRef]
Malghan, V. R. , and Benenson, D. M. , 1973, “Analysis of Cross-Flow Arcs in Transverse Magnetic Fields,” IEEE Trans. Plasma Sci., 1(3), pp. 38–46. [CrossRef]
Schrade, H. O. , 1973, “Stable Configuration of Electric Arcs in Transverse Magnetic Fields,” IEEE Trans. Plasma Sci., 1(3), pp. 47–54. [CrossRef]
Phillips, R. , Geister, D. , Handy, P. , and Bowen, S. , 1964, “The Dynamic Arc in Axial Flow,” Three Phase AC—Arc Heater, University of Michigan, Ann Arbor, MI, Chap. III.
Zhukov, M. F. , and Zasypkin, I. M. , 2007, “Mathematical Methods of Investigating Arc Discharges,” Thermal Plasma Torch Design, Characteristics and Applications, Cambridge International Science Publishing, Cambridge, UK, pp. 116–137.
Hodnett, P. F. , 1969, “Stationary Electric Arc in a Cross-Flow and Transverse Magnetic Field,” Phys. Fluids, 12(7), pp. 1441–1451. [CrossRef]
Sebald, N. , 1980, “Measurement of Temperature and Flow Fields in Magnetically Stabilized Cross-Flow N2 Arc,” Appl. Phys., 21(3), pp. 221–236. [CrossRef]
Romans, W. C. , and Myers, T. W. , 1967, “Experimental Investigation of an Electric Arc in Transverse Aerodynamic and Magnetic Fields,” AIAA Paper No. 67-98.
Nicolai, L. M. , and Kuethe, A. M. , 1969, “Properties of the Magnetically Balanced Arc,” Phys. Fluids, 12(10), pp. 2072–2082. [CrossRef]
Szente, R. N. , Munz, R. J. , and Drouet, M. G. , 1988, “Arc Velocity and Cathode Erosion Rate in a Magnetically Driven Arc Burning in Nitrogen,” J. Phys. D: Appl. Phys., 21(6), pp. 909–913. [CrossRef]
Chau, S. W. , Hsu, K. L. , Lin, D. L. , and Zeng, C. C. T. , 2007, “Experimental Study on Copper Cathode Erosion Rate and Rotational Velocity of Magnetically Driven Arcs in a Well-Type Cathode Non-Transferred Plasma Torch Operating in Air,” J. Phys. D: Appl. Phys., 40(7), pp. 1944–1952. [CrossRef]
Essiptchouk, A. M. , Sharakhovsky, L. I. , and Marotta, A. , 2000, “A New Formula for the Rotational Velocity of Magnetically Driven Arcs,” J. Phys. D: Appl. Phys., 33(20), pp. 2591–2597. [CrossRef]
Lancaster, J. F. , 1986, “The Electric Arc,” The Physics of Welding, 2nd ed., Pergamon Press, Oxford, UK, pp. 139–140.
Jog, M. A. , Cohen, I. M. , and Ayyaswamy, P. S. , 1992, “Electrode Heating in a Wire-to-Plane Arc,” Phys. Fluids B, 4(2), pp. 465–472. [CrossRef]
Sripada, S. S. , Ayyaswamy, P. S. , and Cohen, I. M. , 1998, “Weakly Ionized Plasma Arc Heat Transfer Between Geometrically Dissimilar Electrodes,” ASME J. Heat Transfer, 120(4), pp. 939–942. [CrossRef]
Qin, W. , Cohen, I. M. , and Ayyaswamy, P. S. , 2000, “Charged Particle Distributions and Heat Transfer in a Discharge Between Geometrically Dissimilar Electrodes: From Breakdown to Steady State,” Phys. Plasmas, 7(2), pp. 719–728. [CrossRef]
Maecker, H. H. , 2009, “Cylindrical Arc,” The Electric Arc: The Physics of Stationary Gas Discharges Near Thermal Equilibrium, H. Popp , ed., Matlab GmbH, Berg, Germany, pp. 2/7–2/30.
Hsu, K. C. , and Pfender, E. , 1984, “Modeling of a Free-Burning, High-Intensity Arc at Elevated Pressures,” Plasma Chem. Plasma Process., 4(3), pp. 219–234. [CrossRef]
Gonzalez, J. J. , Bouaziz, M. , Razafinimanana, M. , and Gleizes, A. , 1997, “The Influence of Iron Vapour on an Argon Transferred Arc,” Plasma Sources Sci. Technol., 6(20), pp. 20–28. [CrossRef]
Freton, P. , Gonzalez, J. J. , and Gleizes, A. , 2000, “Comparison Between a Two- and a Three-Dimensional Arc Plasma Configuration,” J. Phys. D: Appl. Phys., 33(19), pp. 2442–2452. [CrossRef]
Belinov, M. S. , and Naidis, G. V. , 2010, “What is the Mathematical Meaning of Steenbeck's Principle of Minimum Power in Gas Discharge Physics?,” J. Phys. D: Appl. Phys., 43(17), p. 175204. [CrossRef]
Lowke, J. J. , 1979, “Simple Theory of Free-Burning Arcs,” J. Phys. D: Appl. Phys., 12(11), pp. 1873–1886. [CrossRef]
Churchill, S. W. , and Bernstein, B. , 1977, “A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow,” ASME J. Heat Transfer, 99(2), pp. 300–306. [CrossRef]
Quemeneur, J. , Freton, P. , Masquere, J. J. , Gonzalez, M. , and Joyeux, P. , 2015, “Cathode Arc Root Movement: Models Comparison,” Plasma Phys. Technol., 2(2), pp. 187–190. https://ppt.fel.cvut.cz/articles/2015/quemeneur.pdf
Desyatkov, G. A. , Engelsht, V. S. , Gurovich, V. T. , and Spektorov, V. L. , 1991, “Theoretical Investigation of Evolution of a Long Arc in External Fields,” 10th International Symposium on Plasma Chemistry (ISPC), Bochum, Germany, Aug. 4–9, pp. 1–6.
Abramowitz, M. , and Stegun, I. A. , 1965, “Bessel Functions of Integer Order,” Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, Dover, Mineola, NY, Chap. 9.
Nemchinsky, V. , 2016, “Temperature Created by a Moving Heat Source That Heats and Melts the Metal Plate (Plasma Arc Cutting),” ASME J. Heat Transfer, 138(12), p. 122301.

Figures

Grahic Jump Location
Fig. 1

Geometric parameters of the electrode-induced magnetic field

Grahic Jump Location
Fig. 2

Boundary conditions for bounded and unbounded domains

Grahic Jump Location
Fig. 3

Parameters S, Smax, and rmax as a function of a and α: (a) rmax function of a and α, (b) Smax function of a and α, and (c) S0 function of a and α

Grahic Jump Location
Fig. 4

Isotherms for the bounded domain for a = 5 mm: (a) isotherms: bounded case with α = 100 m−1 and (b) isotherms: Bounded case with α = 400 m−1

Grahic Jump Location
Fig. 5

Arc velocity with respect to magnetic field for 100 A. (Dashed line): Experimental results from Ref. [12].

Grahic Jump Location
Fig. 6

Arc velocity with respect to current for parallel rails. (Dashed line): MHD simulation results from Ref. [26].

Grahic Jump Location
Fig. 7

Isotherms for a fixed arc with α = 50 m−1 and a = 5 mm and an exponential current density

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