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Mathematical modeling of a direct current electric arc: Part II. Dimensionless representation of a direct current arc

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Abstract

A mathematical model presented in Part I of this work is used to describe fluid-flow, heat-transfer, and electromagnetic phenomena in the arc region of a direct current electric arc furnace (DC EAF). From the analysis of the system, the effects of the arc current and the arc length on the arc characteristics and arc bath interactions can be represented analytically in a rather generalized way, based on the finding that the arc shape is unique (defined with the location of the 10,000 K isotherm) when plotted in the appropriate dimensionless form. This dimensionless arc expansion (only restricted to arcs burned between graphite electrodes in air and outside the region where the arc jet impinges on the bath surface) gives the possibility to derive a unique arc description regardless of the values of the arc current and arc length. Dimensionless correlations representing the relationships among important arc characteristics and arc-bath interactions are derived in this work. These expressions may be used to estimate process variables without the need to run complex numerical calculation.

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Abbreviations

Θ Θ :

azimuthal magnetic flux density (Tesla)

B 0max :

maximum magnetic flux density value at a specific axial distance (Tesla)

B max :

maximum magnetic flux density value in the entire domain (Tesla)

I :

arc current (A)

J :

current density (A/m2)

J c :

current density at the cathode spot (A/m2)

J max :

maximum current density at the bath surface (A/m2)

J z :

axial component of current density (A/m2)

L :

arc length (m)

P :

arc pressure (N/m2)

P max :

maximum arc pressure at the bath surface (N/m2)

q :

heat flux at the bath surface (W/m2)

q max :

maximum heat flux at the bath surface (W/m2)

R :

radial position (m)

R c :

cathode spot radius (m)

R a :

arc radius (m)

T :

arc temperature (K)

T 0max :

maximum temperature at a specific axial position (K)

T max :

maximum temperature in the entire domain (K)

V z :

axial component of velocity (m/s)

V 0max :

maximum value of axial velocity at a specific axial position (m/s)

V max :

maximum axial velocity in the entire domain (m/s)

Z :

axial position (m)

μ 0 :

magnetic permeability (Henry/m)

ρ :

plasma density (Kg/m3)

τ :

shear stress at the bath surface (N/m2)

τ max :

maximum shear stress at the bath surface (N/m2)

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Authors and Affiliations

  1. the Graduate Center in Metallurgy, Instituto Technológico de Morelia, 1500 VP 58120, Morelia, Mich., México

    Marco Ramírez (Professor) & Judith Garduño-Esquivel (Graduate Student)

  2. CINVESTAV-IPN Unidad Querétaro, C.P. 76230, Querétaro, Qro., México

    Gerardo Trapaga (Professor)

Authors
  1. Marco Ramírez
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  2. Judith Garduño-Esquivel
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  3. Gerardo Trapaga
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Ramírez, M., Garduño-Esquivel, J. & Trapaga, G. Mathematical modeling of a direct current electric arc: Part II. Dimensionless representation of a direct current arc. Metall Mater Trans B 35, 373–380 (2004). https://doi.org/10.1007/s11663-004-0037-1

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  • DOI: https://doi.org/10.1007/s11663-004-0037-1

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