dc arc furnace

Transaction

Paper

Introduction

Direct-current (DC) plasma arc furnaces areseeing increased industrial use in the field ofore smelting, particularly for ferrochrome andferronickel applications1,2. Scaling up to highpower levels for new greenfield plants hasnecessitated multiple-cathode designs whichare capable of carrying twice or more thecurrent of traditional single-electrode furnaces,while at the other end of the spectrum interesthas developed for retrofitting existing furnacevessels of various types for DC operation – onemethod of accomplishing this is the dual-electrode concept3,4 as shown in Figure 1.

The dual-electrode furnace uses twographite electrodes, one connected as cathode,the other as anode. Electric current is passedfrom the DC rectifier to the anode, through aplasma arc to the molten bath, through thebath, and through a second arc at the cathode,which is connected back to the rectifier tocomplete the circuit.

This type of furnace has severaladvantages4, key among them being the abilityto avoid using a conductive hearth anode.Hearth anodes are specialized designs uniqueto DC furnaces, and would require a completerebuild of the furnace shell and lining togetherwith any licensing and specialised manufac-turing required for the anode design used. Thiswould add considerably to the capital cost inthe case of a retrofit.

The avoidance of the hearth anode designdoes, however, come with some penalties4.The presence of two arcs (and two arcattachment zones on the slag bath) connectedin series means that the furnace will typicallyoperate at higher voltages compared to asingle-electrode design at comparable powerand arc lengths. Additionally, magneticinteraction between the two arcs results in arepulsive force acting on the arc jets, causingdeflection of the arc columns away from thecentre line of the furnace and toward thesidewalls. This can cause secondary flowpatterns in the both the gas and liquid phasesin the vessel, which result in additionalthermal loading on the furnace lining in theregions adjacent to the two electrodes.

Similar problems occur in three-electrodecircular AC furnaces. The negative effects canbe mitigated in such furnaces by moving to abrush arc mode of operation, in which thedistance between the tip of the electrodes andthe molten bath surface is substantiallyreduced. The brush arc mode retains many ofthe advantages of DC open-arc open-bathoperation, and has been successfullyimplemented on industrial ferroalloy ACfurnaces5,6. It is therefore of some interest toexamine the effect of reducing the arc lengthon the behaviour of the dual-electrode DCfurnace.

It should be noted that operating underbrush arc conditions can potentially introduceadditional difficulties. Due to the proximity ofthe electrodes to the molten slag, splashingand vertical movement of the bath surface maychange the arc length or even extinguish thearc temporarily, resulting in large fluctuationsin the electrical parameters of the furnace;

The dual-electrode DC arc furnace–modelling brush arc conditionsby Q.G. Reynolds*

SynopsisThe dual-electrode DC arc furnace, an alternative design using ananode and cathode electrode instead of a hearth anode, was studiedat small scale using computational modelling methods. Particularattention was paid to the effect of two key design variables, the arclength and the electrode separation, on the furnace behaviour. It wasfound that reducing the arc length to brush arc conditions was a validmeans of overcoming several of the limitations of the dual-electrodedesign, namely high voltages and arc deflection.

Keywordspyrometallurgy, furnace, DC, reverse polarity, dual-electrode, brusharc.

* Mintek, Johannesburg, South Africa.© The Southern African Institute of Mining and

Metallurgy, 2012. ISSN 2225-6253. Paper receivedJan. 2012; revised paper received Mar. 2012.

605The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 112 JULY 2012 �

The dual-electrode DC arc furnace–modelling brush arc conditions

these would need to be appropriately accounted for andlimited in the control methodology used. Splashing of moltenprocess material onto the electrodes may also be exaggeratedat short arc lengths and cause increased electrode wear bychemical and thermal erosion – this problem is, however, wellunderstood from AC furnace experience.

An additional problem with moving to brush arcoperation is the potential for the arc jet direction to becomereversed (that is, the arc gases begin to flow from the surfaceof the bath up toward the electrode, rather than from theelectrode surface down toward the bath). This can occur sincethe electrode surface and bath surface look increasingly liketwo flat, parallel, symmetric plates relative to the dimensionsof the arc as the arc length is reduced, and the directionalityof the arc jet flow is determined primarily by the geometricasymmetry of the conducting surfaces4. Some examples fromhigh speed imaging of DC plasma arcs in a flow-reversalcondition at short arc lengths are shown in Figures 2 and 3.For this work, an Olympus iSpeed 3 high-speed digital videocamera was used to film the arc. The camera used a 200 mmf/22 lens, and was set to record at 5000 frames per secondand 4 μs shutter speed.

Test work has indicated that increasing the furnacecurrent increases the arc jet’s tendency to travel in the usualdirection, from electrode surface down to bath. In general thearc is considerably more unsteady at higher currents, but thejet direction as shown in Figures 4 and 5 is clearly fromelectrode to bath.

�

606 JULY 2012 VOLUME 112 The Journal of The Southern African Institute of Mining and Metallurgy

Figure 1—Schematic of traditional DC (left) vs dual-electrode DC (right) furnaces

From DCRectifier

CathodeElectrode

e–

e– e–

e–

CathodeElectrode

AnodeElectrode

To DCRectifier

To DCRectifier

From DCRectifier

Figure 2—Arc at anode electrode, 1 kA, 20 mm arc length, 200 mmelectrode




This change is most likely due to the fact that the forcesthat act on the arc scale in proportion to the square of thecurrent, and small asymmetries in the geometry are greatlyexaggerated at higher current levels. Such jet reversal issuesare therefore not expected to occur in industrial-scalefurnaces operating at a few kiloamperes or more.

Plasma arc model

Direct current plasma arcs are strongly coupled problems.Separate models of fluid flow, energy transfer, and electro-magnetism are needed, and must be solved simultaneouslyusing numerical methods in order to obtain an overall modelof arc behaviour. The governing equations as used in thepresent work are given below.

Fluid flow:

[1]

[2]

Heat transfer:

[3]

Electromagnetic fields:

[4]

[5]

[6]

wherev is the plasma velocity vectort is timep is the reduced pressure (=P/ρ)μ is the plasma viscosityρ is the plasma densityj is the current density vectorB is the magnetic field vectorT is the plasma temperatureκ is the plasma thermal conductivityCp is the plasma heat capacityσ is the plasma electrical conductivityQR is the volumetric radiation energy lossφ is the scalar electric fieldμ0 is the free-space magnetic permeability.

Both σ and QR are strong functions of the plasmatemperature T.

These equations must be solved using an appropriatenumerical scheme that takes into account the strong timedependence of the arc evolution problem as well as thecoupling effects. The various fields must also be suppliedwith appropriate initial and boundary conditions for theparticular problem being studied. The models are solved inthree dimensions in order to fully capture the spatialbehaviour and interactions of the arcs. Further details can befound in earlier publications7,8.

For the dual-electrode case, the electrical boundaryconditions and solution region are shown in Figure 6. Currentdensity (the local gradient of the electric potential field) isspecified on each of two arc attachment zones for the anodeand cathode arcs as equal and opposite in magnitude, tosimulate the passage of current down one electrode and upthe other in the dual arrangement. Current density at the arcattachment zones is taken as jk = 3.5 kA/cm2 from Bowman'swork9. The roof and walls are assumed to be electricallyinsulating, and the bath surface is assumed to be at groundpotential.

The numerical algorithm was implemented in ANSI Ccode and compiled for execution on computers running 32-bitUbuntu Linux 10.04 using GCC 4.3.1. The FFTW library10

was used to accelerate parts of the solver routine, and theOpenMP library provided multi-threaded parallelization.

The common simulation parameters used for all dual-electrode test cases are shown in Table I. The physicalproperty data assumes air as the plasma gas. Table II showsthe range of arc length (equal to the simulation regionheight) and electrode separations (the distance betweenelectrode centre lines) tested for the brush arc study. Everycombination of these two parameters was tested, resulting in40 simulations in total.

The dual-electrode DC arc furnace–modelling brush arc conditionsTransaction

Paper

607The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 112 JULY 2012 �

Table I

Common parameters used in all dual-electrode models

Parameter Value Parameter Value

Region length 0.2 m TWALL 2000 KRegion width 0.1 m TSURFACE (BATH) 3000 KElectrode O.D. 0.05 m TSURFACE (ELECTRODE) 4100 Kμ 1.307 x 10-4 Pa.s Grid resolution Up to 384 x 192 x 96ρ 0.02593 kg/m3 Simulation time 10 msκ 3.067 W/m.K jk 3.5 x 107 A/m2

CP 9420 J/kg.K Current 250 A

Figure 6—Electrical boundary conditions used for the computationalmodel


Each simulation was run for 10 ms of model time frominitial conditions (arc ignition). Some parts of the dataanalysis required time-averaged values of the fields in themodel – in these cases, a time average of the last 2 ms wastaken.

Results and discussion

Variation of temperature distribution

Figures 7 to 11 show qualitatively the effect of changing thearc length from longest to shortest at a fixed electrodeseparation of 0.04 m. Projected time-averaged temperaturefields show the maximum value of T in the y-axis direction,reducing the field dimensionality from 3D to 2D. The scaleshown ranges from 2000K (white) to 15000K (black).

Several changes are visible as the arc length is reduced tobrush arc conditions. Firstly, the arcs become more localizedin space, with greatly reduced thermal interaction in both thespace between them and the region surrounding them. Thisis due to more compact recirculation patterns developingaround the arc jets as they become confined by the electrodeand bath surfaces at short arc lengths, which act to hold thehot plasma gases closer to the arc column. Secondly, due tothe shortened distance the jets have to travel before theyreach the bath surface, the arcs do not appear to deflect eachother as much at shorter arc lengths.

Magnetic field consistency check

One of the primary aims of the brush arc test cases is toexamine the effects of interaction and deflection of the arcs,and it is therefore important to verify that the magnetic fieldcalculations in the model are being performed in a consistentand repeatable way. The self-magnetic field around the arccolumns (together with the current density field from which itis derived) is the source of the deflection forces that act topush the arc jets apart. Some examples of the three-dimensional magnetic field at different arc lengths are shownin Figures 12 to 14.

�


Table II

Brush arc test parameters

dE, electrode separation LA, arc length

0.02 m 4.2 mm0.03 m 8.3 mm0.04 m 16.7 mm0.05 m 33.3 mm0.06 m 50 mm0.07 m0.08 m0.09 m

Figure 11—Projected temperature field, 0.04 m separation, 4.2 mm arclength


Figure 9—Projected temperature field, 0.04 m separation, 16.7mm arclength


Figure 7—Projected temperature field, 0.04 m separation, 50 mm arclength

Figure 12—Absolute values of magnetic field vector, 0.05 m separation,4.2 mm arc length

Figure 13—Absolute values of magnetic field vector, 0.05 m separation,16.7 mm arc length

Figure 14—Absolute values of magnetic field vector, 0.05 m separation,50 mm arc length

The calculated peak magnitudes of the magnetic fields,which are generally found only within the core of the arcattachment zones on the electrode surfaces, lie within 3.5 percent of each other across a wide range of arc lengths. Thissuggests that the magnetic and electric fields are beingpredicted consistently at different arc lengths, and the changein region dimensions is not adversely affecting thecalculation.

An additional cross check is shown in Figure 15, for anelectrode separation of 0.05 m (defined as the centre-to-centre distance between electrodes). Here, the magnetic fieldprofile in the x-direction at the top surface of the calculationregion, along the centre line of the two arcs, is given for allarc lengths tested. The curves lie very close together,confirming that the magnetic field calculation, and thereforearc deflection calculation, is consistent across different arclengths.

Voltage behaviour

As the arc length is reduced to brush arc conditions, thesystem voltage (calculated as the difference between themaximum and minimum of the electric potential field) for thedual-electrode configuration reduces considerably. Evolutionof the voltage over the duration of the simulation for selectedexample cases is shown in Figure 16.

Much higher voltages are obtained with longer arcs. It isinteresting to note that the voltage in the case of arc lengthLA = 50 mm does not appear to have reached steady state bythe end of the simulation, suggesting that an increased runtime would show even greater disparities.

Calculating time-averaged voltages and comparing all the dual-electrode model cases gives the results shown inFigure 17.

The gross behaviour of voltage increasing with increasingarc length is confirmed by these results; however, the shapeof the curves has some interesting subtleties. In general, atlarge dE the voltage remains constant with separation for agiven arc length. As dE decreases, the voltage first risesslightly, and then drops (this is particularly noticeable atlonger arc lengths). The reason for this is that as the arcs arebrought closer together they repel each other more, causingmore deflection. The increased deflection results in a longercurrent path and hence an increase in system voltage. Thiseffect is, however, rapidly mitigated when the arcs are placedin extreme proximity to one another, as the gas in the regionbetween them becomes heated to the point at which it startsto conduct electricity. This results in some of the current flowshort-circuiting directly between the arcs4 instead oftravelling through the bath, reducing the length of the currentpath significantly and causing the voltage to drop.

Arc deflection

The absolute deflection is defined as the separation betweenthe two arc columns at the level of the molten bath. Arcdeflection occurs in the dual-electrode models as a result ofelectromagnetic interaction between the two arc columnscarrying current in opposite directions. It is measured bycalculating a time-averaged three-dimensional temperaturefield for each case, and then finding the distance between thetwo temperature maxima at the bath surface (lower boundaryin the model). This value is compared across all dual-electrode model cases in Figure 18.

It can be seen that decreasing the arc length to brush arcconditions greatly reduces the absolute deflection, partic-ularly at smaller electrode separation values. The minimum inabsolute deflection also moves closer to the centre of thefurnace as the arc length is reduced.


Paper

The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 112 JULY 2012 609 �

Figure 16—Dual-electrode voltage behaviour as a function of time,electrode separation 0.08 m

Figure 17—Variation of system voltage with arc length and electrodeseparation

Figure 15—Magnitude of magnetic field vectors along top boundary ofregion, through centrelines of electrodes


Arc deflection can also be calculated using a relativedefinition, which normalizes the data relative to thedimensions of the arc and system being studied. Oneintuitive way to do this is to calculate the angle at which thearc jets are deflected. This is done using the formula below:

[7]

Here, θA is the arc deflection angle, and sE is the absolutedeflection as defined above. The arc deflection angle ismeasured between the arc column and the vertical. Thevariation of the deflection angle with model parameters for alldual-electrode model cases is shown in Figure 19.

Reducing the arc length has somewhat less of an effecton the arc deflection angle than it does on the absolutedeflection; however, there is still a noticeable trend to lowerangles (more vertical arc columns) at shorter arc lengths. Apossible explanation for this phenomenon is that the arc jetinitially travels nearly perpendicularly to the surface of theelectrode due to the very high velocities imparted by theLorentz forces (which arise due to the interaction betweenthe arc current j and the self-magnetic field B) in theimmediate vicinity of the arc attachment spot, and onlyfurther down the column do the magnetic repulsion effectsfrom the opposite arc column start to dominate and push thejets apart. Some qualitative evidence of this can also be seenin the temperature profiles shown in Figures 7 to 11.

Lateral blast

Lateral blast is defined as the peak velocity of the arc gasesin the horizontal direction. For the purposes of the presentstudy, the lateral blast is measured in a vertical planepositioned at the outer edge of the electrodes. This valuegives a measure of how much momentum is imparted to thegases in the furnace freeboard by the deflection of the arccolumns, and gives an indication of the degree to which thehot gases and molten slag in the bath will be driven towardthe furnace sidewalls.

Figures 20 and 21 show 3D plots of the x-component ofthe time-averaged velocity field for an example model case.Areas of strong horizontal velocity are visible in red and blue,near to the bath surface at the bottom of the region.

�


Figure 18—Absolute arc deflection as a function of arc length andelectrode separation

Figure 19—Arc deflection angle as a function of arc length andelectrode separation

Figure 20—Section of velocity field through electrode centrelinesshowing vx, electrode separation 0.05 m, arc length 50 mm

Figure 21—Lateral blast region at lower right, electrode separation 0.05 m, arc length 50 mm

Lateral blast values for all dual-electrode model caseswere calculated using time-averaged velocity fields and arecompared in Figure 22.

Lateral blast velocities are seen to decrease both as theelectrode separation increases, and as the arc lengthdecreases. The effect of reducing arc length is pronounced,with the lateral blast falling away to negligible levels for theshortest arc lengths tested. This result is predominantly dueto two effects. Firstly, as the electrode separation increases,the deflection of the arc columns decreases, causing less ofthe arc jet to be diverted toward the furnace sidewalls.Secondly, decreasing the arc length results in smaller, morecompact recirculation zones around the arc jet as it isconfined between the electrode and bath surfaces—as aresult, most of the arc gases are drawn back into the arcbefore they can impart much momentum to the surroundingfluids.

Conclusions

The dual-electrode furnace has been modelled at small scaleusing computational methods. This model has beensuccessfully applied to a study of the effect of certainimportant design variables, namely electrode separation andarc length, on the behaviour of and interactions between thearc columns at the anode and cathode electrodes.

Accuracy of the magnetic field calculation across a rangeof arc lengths was verified. Results of the system voltagecalculations showed a very strong dependence of voltage onarc length, with shorter brush arc lengths consistentlyproducing the lowest voltages. Deflection of the arc columnsaway from each other in accordance with theoreticalunderstanding was confirmed qualitatively using visual-izations of the temperature fields. Deflection was alsomeasured quantitatively, and found to be reduced at short arclengths. A side effect of deflection, lateral blast velocity,confirmed this result with much lower velocities beingpredicted in the models at short arc lengths.

In summary, the modelling work conducted suggests thatoperating dual-electrode type furnaces in brush arcconditions is potentially a means of overcoming several

limitations of the design. Some additional difficulties may beintroduced, but it is expected that careful design of thecontrol system and electrodes would be able to address theseissues.

Future work should include experimental testing of thedual-electrode concept at pilot scale. Visual and electricalmeasurements during such a test campaign wouldcomplement the largely theoretical results presented here.

Acknowledgements

This paper is published by permission of Mintek. The authorwould also like to thank GLPS for productive discussions andpermission to use the photographs in Figures 2 to 5.

References

1. SAGER, D., GRANT, D., STADLER, R., and SCHREITER, T. Low cost ferroalloy

extraction in DC-arc furnace at Middleburg Ferrochrome. Journal of the

Southern African Institute of Mining and Metallurgy, vol. 110, no. 12,

December 2010. pp. 717–724.

2. NAUDE, C.P. and SHAPIRO, M.D. Implementation of the first commercial scale

DC smelter for ferronickel production from low grade laterite ores—

technology building blocks and lessens learned. Journal of the Southern

African Institute of Mining and Metallurgy, vol. 110, no. 12, December

2010. pp. 725–732.

3. GREYLING, F.P. and GREYLING, H.W. DC Brush Arc Furnace for Ferrochrome

Production. South African Patent Application 2010/06472, 2010.

4. REYNOLDS, Q.G. The dual-electrode DC arc furnace—modelling insights.

Journal of the Southern African Institute of Mining and Metallurgy,

vol. 111, no. 10, October 2011. pp. 697–703.

5. WALKER, C., SUTHERLAND, K., MARSHALL, B., GELDENHUIS, J.M.A., ELS, J.,

VOERMANN, N., and WASMUND, B. Conversion to partially open bath smelting

on Highveld ironmaking furnaces. Proceedings of the European

Metallurgical Conference 2007, June 11–14, Dusseldorf (Germany), 2007.

pp. 895–914.

6. STEINBERG, W.S. Development of a control strategy for the open slag bath

furnaces at Highveld Steel and Vanadium Corporation Ltd. MIng disser-

tation, University of Pretoria (South Africa), 2008.

7. REYNOLDS, Q.G., JONES, R.T., and REDDY, B.D. Mathematical and computa-

tional modelling of the dynamic behaviour of direct current plasma arcs.

Journal of the Southern African Institute of Mining and Metallurgy,

vol. 110, no. 12, December 2010. pp. 733–742.

8. REYNOLDS, Q.G. and REDDY, B.D. Some aspects of dynamic computational

modelling of direct current plasma arc phenomena. Proceedings of Coupled

Problems 2011, June 20–22, Kos Island (Greece), 2011. Paper no. p. 135.

9. BOWMAN, B. Properties of arcs in DC furnaces. Proceedings of the 52nd

Electric Furnace Conference, November 13–16, Nashville (USA), 1994.

pp. 111–120.

10. http://www.fftw.org. �


Paper

The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 112 JULY 2012 611 �

Figure 22—Lateral blast as a function of arc length and electrodeseparation

Documents

dc arc furnace