A mathematical model of the cathode region of a high intensity carbon arc

McKelliget, J.; Szekely, J.

doi:10.1088/0022-3727/16/6/010

Cited by 30 publications

(23 citation statements)

References 11 publications

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“…In the model presented in this report the arc is treated as a fluid [1][2][3][4][5][6][7][8][9][10][11][12] with temperature-dependent thermodynamic properties. 15,16) The coupled conservation equations of energy, mass and momentum, which define plasma temperature, pressure and velocity, are solved together with Maxwell's equations.…”

Section: Mathematical Model Of a DC Electric Arcmentioning

confidence: 99%

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Modeling of a DC Electric Arc Furnace. Heat Transfer from the Arc.

et al. 2000

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A mathematical model describing heat and fluid flow in an electric arc has been developed and used to predict heat transfer from the arc to the steel bath in a DC Electric Arc Furnace. The arc model takes the separate contributions to the heat transfer from each involved mechanism into account, i.e. radiation, convection, condensation and energy transported by electrons. The model predicts heat transfer for different currents and arc lengths. Model predictions show that arc efficiency is higher for lower power input. The model also predicts shear stresses and current density distribution at the steel surface. This information can be used as boundary condition input to simulate the effect of heating with electrodes in a DC EAF on the heat and fluid flow in the steel bath.KEY WORDS: modeling; arc; heat transfer.model. More specifically these authors used three different methods to determine the Lorentz forces responsible for the fluid flow. These methods are i) The Laplace equation for electric potential ii) the magnetic diffusion equation, and iii) the complete magnetic transport equation. The first two methods, however, do not include the induced electric field term, vϫB, in the solution. Assuming that the magnetic Reynolds number is much less than unity, these methods give a good approximation of the Lorentz forces. However, this is not always the case for high-current arcs, as in the case of EAFs. The third method does include this term, but a disadvantage with this method is that the system of equations becomes more difficult to solve. In the present work, the Poisson equation for electric potential is used to overcome these problems since the induced electric field is included and the current in the system can be correctly described. Mathematical Model of a DC Electric ArcIn the model presented in this report the arc is treated as a fluid [1][2][3][4][5][6][7][8][9][10][11][12] with temperature-dependent thermodynamic properties. 15,16) The coupled conservation equations of energy, mass and momentum, which define plasma temperature, pressure and velocity, are solved together with Maxwell's equations. First the problem is stated and a description of the fluid-flow model is provided. Then source terms, boundary conditions and heat transfer mechanisms are discussed. Statement of the ProblemIn Fig. 1 a schematic representation of the region of integration of the DC arc model is given. The system consists of the cathode (graphite electrode), the arc column, and the anode (steel bath). The calculation domain is defined so as to allow for entrainment and general interaction with the surrounding gases. Mathematical Formulation of the FlowThe following assumptions are made in the statement of the mathematical model of a DC arc:• The arc is axis symmetric.• The operation of the arc is independent of time, i.e. steady state.• The arc is in local thermal equilibrium (LTE), 17) i.e. the electron and heavy-particle temperatures are very similar. This assumption has been shown to be valid throughout most of a gas tungsten ...

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Section: Mathematical Model Of a DC Electric Arcmentioning

confidence: 99%

“…In the past, several individual models of electric arcs, EAF steel baths, and stirred ladles have been developed. [1][2][3][4][5][6][7][8][9][10][11][12] Coupling of these models is necessary in order to achieve accurate prediction of heating effects in EAFs and LFs.…”

Section: Introductionmentioning

confidence: 99%

Modeling of a DC Electric Arc Furnace. Heat Transfer from the Arc.

et al. 2000

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“…In this model, the arc is treated as a fluid 5,[11][12][13][14][15] with temperature-dependent properties. [16][17] The coupled equations for conservation of energy, mass and momentum, which define the plasma temperature, pressure and velocity are solved.…”

Section: The Modeling Of the Arcmentioning

confidence: 99%

Heating and Electromagnetic Stirring in a Ladle Furnace. A Simulation Model.

2000

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A three-dimensional simulation model coupling heating and induction stirring in an ASEA-SKF ladle furnace was developed. Data of the heat transfer from the arcs to the steel bath were predicted in a separate model and included as boundary conditions in a ladle model. The arc model considers the contributions of heat transferred by of each of the following mechanisms: radiation, convection, condensation and energy transported by electrons. Predictions were made to simulate the change of temperature distribution in the ladle during simultaneous heating with electrodes and stirring by induction. A first attempt was made to compare the predictions with measured temperatures from a 100 t ASEA-SKF ladle. The agreement was found to be fairly good when heat-flux data for a 25 cm arc length were used as input to the ladle model. This indicates that the model can be used for more in-depth studies of the effects of heating for ladles that are inductively stirred.

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“…[6] Due to its small size relative to the rest of the arc, the cathode region can THE main goal of this work is to demonstrate a new be assumed to be isothermal, in contrast to other regions technique of order-of-magnitude scaling (OMS) [1] to a comin the domain, where significant temperature gradients are plex engineering problem: the welding arc. This technique present.…”

Section: Introductionmentioning

confidence: 99%

“…Dimensional analysis provides of these have been derived using dimensional analysis or an exact description of the functional dependence in the asymptotic analysis. [6][7][8][9][10][11][12][13][14] In addition, some contributions to problem, based on a complete set of dimensionless groups.…”

Section: Introductionmentioning

confidence: 99%

Order-of-magnitude scaling of the cathode region in an axisymmetric transferred electric arc

Méndez

Eagar

Ramírez

et al. 2001

Metall Mater Trans B

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A new technique of order-of-magnitude scaling (OMS) has been applied to the mathematical modeling of the cathode region of a long gas tungsten arc (GTA). The estimations obtained are combined with numerical calculations; thus, important features of both techniques are considered simultaneously: the high precision of numerical modeling and the generality and simplicity of algebraic expressions. Power-law expressions for the estimations of characteristic unknowns such as maximum pressure in the cathode spot and maximum plasma velocity are obtained and are consistent with previous analytical or asymptotic work. Dimensional analysis is used to identify dimensionless groups governing the system, and asymptotic considerations are used to identify two dimensionless groups (the Reynolds number and the dimensionless arc length) as the most significant ones governing momentum transfer in the cathode region. The estimations obtained are calibrated with functions that depend only on these two most significant dimensionless groups. It is suggested that the numerical results for different cases can be reduced to a single general map.

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A mathematical model of the cathode region of a high intensity carbon arc

Abstract: Through the simultaneous statement of Maxwell's equations, the turbulent Navier-Stokes equations, and the differential thermal energy balance equation, a mathematical representation has been developed for fluid flow and heat transfer in the cathode region of high intensity carbon arcs.

Cited by 30 publications

References 11 publications

Modeling of a DC Electric Arc Furnace. Heat Transfer from the Arc.

Modeling of a DC Electric Arc Furnace. Heat Transfer from the Arc.

Heating and Electromagnetic Stirring in a Ladle Furnace. A Simulation Model.

Order-of-magnitude scaling of the cathode region in an axisymmetric transferred electric arc

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