DC ARC PHOTOGRAPHY AND MODELLING

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1 DC ARC PHOTOGRAPHY AND MODELLING R.T. JONES, Q.G. REYNOLDS nd M.J. ALPORT Pyrometllurgy Division, Mintek, Privte Bg X3015, Rndburg, 15, South Afric E-mil: Applied Physics Group, School of Pure nd Applied Physics, University of Ntl, South Afric ABSTRACT DC rc furnces operte with grphite cthode positioned bove molten slg nd metl bth contined inside furnce vessel. The plsm rc, consisting of ionised prticles t extremely high tempertures, forms conducting pth between the grphite cthode nd the molten bth. The power provided by the rc cn be controlled by djusting the rc length nd the current. The high-intensity plsm rc emntes from reltively smll ttchment re on the grphite electrode, nd extends down to the surfce of the molten bth. Photogrphs of the rc re presented nd compred to models of the shpe of the rc. These models provide description of how the rc voltge vries s function of rc length nd current, for given set of conditions in the furnce. The rc ttchment zone, where the rc impinges on the molten slg surfce, is highly turbulent nd opertes t very high temperture. This promotes very rpid melting, fst rection kinetics, nd effective mixing. The impingement of the rc cuses crter-like depression in the surfce of the slg. This hs significnt effect on the distribution of current in the molten slg, nd the voltge drop cross the slg. The shpe nd size of this depression hs been photogrphed, nd the resulting informtion used in model of the depression. Keywords Pyrometllurgy; extrctive metllurgy; modelling INTRODUCTION The inherent persistency nd intensity of direct-current (DC) plsm rc offers some unique dvntges for number of smelting processes (Jones et l, 1993). DC rc furnces operte with grphite cthode positioned bove molten slg nd metl bth contined inside furnce vessel. The plsm rc, consisting of ionised prticles t extremely high tempertures, forms conducting pth between the grphite cthode nd the molten bth. At tempertures bove bout 5000 K, the constituent molecules of the gs ionise into positively chrged ions nd negtively chrged electrons, giving neutrl but very strongly conductive plsm. This conducting mteril permits electricl current to pss from the furnce electrode through to the furnce bth nd complete the circuit. Flow of the plsm in the rc column is driven very strongly downwrd by electromgnetic forces, in jet from the electrode towrds the molten bth. Much of the energy from the rc is delivered to loclised re directly beneth the rc, mking this very effective wy of heting the process mteril. The power provided by the rc cn be controlled by djusting the rc length nd the current. The open rc provides n dditionl degree of freedom to the supply of energy to the furnce, in tht the resistivity of the slg is no longer solely responsible for the dissiption of energy to het the molten slg. This renders the energy supply nerly independent of slg composition, which my llow the slg chemistry to be optimized for the best recovery of vluble metls (insted of for the required electricl chrcteristics). The high-intensity plsm rc emntes from reltively smll ttchment re on the grphite electrode, nd extends down to the surfce of the molten bth. Photogrphs of the rc hve been compred to models of its shpe. These models provide description of how the rc voltge vries s function of rc length nd current, for given set of conditions in the furnce. The rc ttchment zone, where the rc impinges on the molten slg surfce, is highly turbulent nd opertes t very high temperture. This promotes very rpid melting, fst rection kinetics, nd effective mixing. The

2 impingement of the rc cuses crter-like depression in the surfce of the slg. This is believed to hve significnt effect on the distribution of current nd temperture in the molten slg, nd the voltge drop cross the slg. The shpe nd size of this depression hs been photogrphed, nd the resulting informtion used in model of the depression. STEADY-STATE ARCS The stedy-stte electricl behviour of the DC rc hs been well described previously (Bowmn et l, 1969; Bowmn, 1994), effectively summrizing lrge quntity of dt from DC electricl rcs in the 1 to 10 ka rnge. This work provides description of how the rc voltge vries s function of rc length nd current, for given set of conditions in the furnce. The model uses mesured nd extrpolted rc shpes, fitted to clculted plsm conductivities nd estimted temperture profiles. The high-intensity plsm rc hs been modelled by Bowmn s emnting from reltively smll ttchment re on the grphite electrode, nd extends down to the surfce of the molten bth. This is shown schemticlly in Figure 1. cthode z r k r node Fig.1 Schemtic representtion of DC rc Eqution (1) describes the shpe of the conducting volume of the rc s function of the distnce from the cthode ttchment spot. The ssumptions include n xi-symmetric rc nd no interction effects t the node. r r k z 3.. exp (1) 5r = k The rc rdius, r, vries with the distnce, z, from the cthode surfce. The rdius, r k, of the cthode-spot ttchment is determined by the vlue of the cthode-spot current density, estimted by Bowmn to be round 3.5 ka/cm. Arc dimeter, cm Arc length, cm Fig. 4 ka rc in ir, struck on grphite block Fig.3 Arc dimeter versus length for 4 ka rc

3 The rc shpe function llows the rc voltge to be obtined by integrtion. Severl constnts of Bowmn s long with single vrible prmeter, the rc resistivity, pper in the rc voltge expression. Vrition of the rc resistivity then llows the model to be fitted to pilot or industril plnt dt. The integrtion required is: L j r V k k.. dz r = ρ () π z Z = (3) r k ρ rc resistivity, Ωcm j k cthode-spot current density, ka/cm r k cthode-spot rdius, cm r rc rdius, cm L rc length, cm V rc voltge, V z xil distnce from cthode, cm The finl result of this integrtion is n expression relting the voltge of the rc to its length nd current. This is shown in Eqution (4). V Iρ 1 1 ln( + b) ml ln mπ + b + b.exp( ml) = [ b.exp( ml) ] (4) = 3. r k (4) b =. r k (4b) 1 m = (4c) r k r k I = (4d) π (3500A / cm ) V rc voltge, V I current, A ρ rc resistivity, Ωcm r k cthode-spot rdius, cm L rc length, cm Eqution (4) is depicted grphiclly in Figure 4, which shows rc voltge s function of rc length, for rnge of different currents, t given rc resistivity of Ωcm.

800 700 600 Arc voltge, V 500 400 300 80 ka 60 ka 40 ka 0 ka 00 100 0 0 0 40 60 80 100 Arc length, cm Fig.4 Arc voltge s function of rc length t different currents, for given rc resistivity of 0.

4 Arc voltge, V ka 60 ka 40 ka 0 ka Arc length, cm Fig.4 Arc voltge s function of rc length t different currents, for given rc resistivity of Ωcm Vlues for rc resistivity hve been obtined experimentlly on number of pilot-plnt furnce cmpigns t Mintek. These were obtined by mesuring the voltge while keeping the current constnt nd vrying the rc length. The vlue used for the rc resistivity is tht which best fits the experimentl dt. The resistivity vries substntilly ccording to the previling gs tmosphere in the furnce. For exmple, the presence of zinc vpour mkes the rc more conductive thn crbon monoxide does. DYNAMIC ARCS Observtions of rel rcs (s illustrted in Figures 5 to 9) revel errtic instbilities nd chotic motion. Sometimes, helicl pttern ppers s precursor to full instbility. There re lso periods when the rc becomes diffuse nd ppers to be spred over the entire electrode tip. Clerly, the time-verge of this nonstedy behviour hs significnt bering on the properties of the rcs. Fig.5 Arc bout to become unstble Fig.6 Pretzel-shped rc in ir on grphite block

t 8.1 ka (Imge L16354) Additionl vribles come into ply when the rc is

chnging geometricl rrngement tht encourges the rc to move to new,

In moving to new position, the rc moves extremely rpidly cross the tip of

Figure 10 shows two successive imges (one fiftieth of second prt) in

C0936) Multiple simultneous rcs hve been observed nd recorded, but it

5 Fig.7 Fig.8 Fig.9 Diffuse 7 ka rc onto slg Violent splshing t ka Thicker rc with splshing t 8.1 ka (Imge L16354) Additionl vribles come into ply when the rc is enclosed in hot re-rditing furnce vessel, nd when the rc is struck on molten surfce tht deforms nd splshes. The chnging shpe of the depression in the liquid surfce provides rpidly chnging geometricl rrngement tht encourges the rc to move to new, shorter, more conductive pths. In moving to new position, the rc moves extremely rpidly cross the tip of the electrode. Figure 10 shows two successive imges (one fiftieth of second prt) in which the rc hs moved lmost from one side to the other of 0 cm dimeter electrode. Fig.10 Rpid rc movement in two successive imges 1/50 s prt (Imges C0935 nd C0936) Multiple simultneous rcs hve been observed nd recorded, but it would need higher speed cmer to scertin whether the rcs re truly simultneous or whether they occurred sequentilly during the exposure period, which is usully set to less thn 1/50s becuse of the high intensity of the rc. Fig.11 Two imges ( few minutes prt) showing two rcs simultneously (Imges C079 nd C15) Fig.1 Three simultneous rcs; totl current ka

ARC DEPRESSION The rc jet is seen, from previous mesurements nd modelling work (Bowmn, 198; Bowmn, 1990), to be high-velocity turbulent self-constricted jet.

6 ARC DEPRESSION The rc jet is seen, from previous mesurements nd modelling work (Bowmn, 198; Bowmn, 1990), to be high-velocity turbulent self-constricted jet. The force generted by the impingement of such jet on dense deformble medium cn be very significnt, even t pilot-plnt scle, nd tends to crete cvity t such n interfce. The rc-ttchment zone (AAZ) is therefore not treted s flt surfce but s depressed cvity of prboloidl shpe, s suggested by Bowmn (1994). The determintion of the dimensions of the AAZ depression is ided by n empiricl correltion by Mecker (1955) tht specifies the dependence of DC rc thrust on current flow. For sufficiently long rcs: T I (5) T rc thrust, N I rc current, A The volume of the displced slg, in the prboloid, my be expressed s: π = r h A A (6) V V volume of prboloid, m 3 r A rdius of prboloid depression, m h A height or depth of prboloid depression, m The buoyncy force generted by the bsence of the slg from the cvity cn be tken s the volume multiplied by the slg density nd grvittionl ccelertion. The buoyncy force my be equted to the thrust, in order to provide n expression relting h A to r A. 7 I π gr = ρ h A A (7) ρ - slg density, kg/m 3 g stndrd grvittionl ccelertion, 9.81 m/s One further constrint needs to be imposed on these two dimensions, in order to specify fully the size of the cvity, s function of the rc current. A reltionship between h A nd r A cn either be specified priori or fitted to experimentl dt. It is understood tht the depth cnnot resonbly be expected to exceed the dimeter of the depression in stble cvity. Imges such s Figure 13 llow one to mke quntittive estimte of the dimeter to depth rtio of the rc depression. The imges shown in Figure 14 illustrte the different types of depression tht my be obtined under different circumstnces. Fig.13 Cler imge of rc depression t.9 ka (Imge F00878)

Fig.14 Arc depressions punched hole nd smered depression (Imges C0833, FL05, FL08) According to Bowmn (1994), depressions in liquids tke bout 10 to 100 ms to form.

6 ka (Imge L00683) ELECTRICAL MODEL OF MOLTEN BATH In smelting systems, the slg resistnce cuses voltge drop cross the molten bth.

It is importnt to hve reltively ccurte prediction of the voltge cross the slg before specifying the power supply of new industril furnce.

price of the trnsformer. The slg bth would be esy to model electriclly if it ws known to hve flt surfce nd uniform conductivity, nd if the potentil distribution t the upper surfce ws well understood.

7 Fig.14 Arc depressions punched hole nd smered depression (Imges C0833, FL05, FL08) According to Bowmn (1994), depressions in liquids tke bout 10 to 100 ms to form. Figure 15 shows two depressions existing simultneously, where the rc hs jumped to new position before the previous depression hs hd chnce to die wy. Fig.15 Two rc depressions existing simultneously;.6 ka (Imge L00683) ELECTRICAL MODEL OF MOLTEN BATH In smelting systems, the slg resistnce cuses voltge drop cross the molten bth. If the slg is highly resistive, this voltge drop cn be quite significnt. It is importnt to hve reltively ccurte prediction of the voltge cross the slg before specifying the power supply of new industril furnce. An incorrect specifiction cn cuse the filure of the process, nd n overconservtive specifiction tht will gurntee opertion over wide rnge of conditions my unnecessrily dd significntly to the purchse price of the trnsformer. The slg bth would be esy to model electriclly if it ws known to hve flt surfce nd uniform conductivity, nd if the potentil distribution t the upper surfce ws well understood. A smll zone of constnt high potentil could be envisged where the rc impinges on the surfce, nd zero potentil could be envisged cross the bottom surfce of the bth where it is in contct with molten metl cross the dimeter of the furnce. The Lplce eqution could then be solved to obtin the potentil distribution. However, in relity, the impingement of the rc cuses depression in the surfce of the slg. This hs to be tken into ccount in the model, s it cn lter the geometricl current distribution quite significntly. ARCS AT INDUSTRIAL SCALE The specifiction of the power supply is one of the principl requirements when n industril furnce is bout to be built, nd needs to be in plce bout twelve to eighteen months before the furnce is to be commissioned. The totl power requirement of the furnce is derived from the desired throughput, nd the experimentllydetermined specific energy requirement for the process. The specifiction of the operting rnges for voltge nd current requires more detiled understnding of the scle-up of the furnce design. In the pst, there hs been much specultion bout the behviour of high-current rcs, s some fetures such s thrust depend on the squre of the current. Industril-scle rcs re very difficult (sometimes even dngerous) to photogrph, nd in mny furnces, the rc is never visible. Fortuntely, video imges tken of the high-current rc in n industril steelmking furnce showed very similr behviour to the pilot-scle rcs previously photogrphed. Some smple imges re shown in Figure 16.

Fig.16 Industril steelmking rc t 40 ka, 450 V (full power is t 70 ka, 550 V) ADVANCES IN HIGH-SPEED DIGITAL IMAGING The work presented here includes number of imges tken using stndrd digitl still

The video imges were cptured t rte of 5 frmes per second (t resolution of 768 x 576 pixels), but by seprting the odd nd even scn lines of the interlced PAL video imge, the frme rte ws effectively

High performnce digitl video cmers my cpture imges t rtes from 1 000 to 60 000 frmes per second. This would enble the imging of phenomen tht hppen in millisecond or less to be nlysed in detil.

8 Fig.16 Industril steelmking rc t 40 ka, 450 V (full power is t 70 ka, 550 V) ADVANCES IN HIGH-SPEED DIGITAL IMAGING The work presented here includes number of imges tken using stndrd digitl still cmer s well s with stndrd cmcorder. Welding filters were used to reduce the intensity of the light to mngeble levels. The video imges were cptured t rte of 5 frmes per second (t resolution of 768 x 576 pixels), but by seprting the odd nd even scn lines of the interlced PAL video imge, the frme rte ws effectively doubled to 50 frmes per second. Much higher filming speeds, with very little dely between successive frmes, would be needed in order to cpture some of the fster phenomen. High performnce digitl video cmers my cpture imges t rtes from to frmes per second. This would enble the imging of phenomen tht hppen in millisecond or less to be nlysed in detil. Short exposure times permit the digitl video cmer to cpture extremely fst-moving objects on ech frme of the video. Clssiclly, high-speed photogrphy used to be performed with the id of strobe lighting, which gve exposure times down to frctions of millisecond. With the modern electronics vilble in high-speed digitl video cmers, exposure times of s low s 10 microseconds re vilble without the need for high-intensity strobes tht would otherwise be required to freeze events tht re evolving rpidly in time. High-resolution imges, up to 104 x 104 pixels in size, vilble in modern CMOS-design digitl video cmers, provide sufficient detil for ccurte imge nlysis nd trcking of smll-scle fetures from frme to frme. CONCLUSIONS A number of criticl res hve been identified where n incresed understnding is required. The most importnt of these is the need to better understnd the energy trnsfer in the furnce, closely followed by n bility to correctly specify the requirements of the electricl power supply. Higher-speed digitl video imging would mke vluble contribution towrds chieving these objectives. Dynmic mthemticl modelling of rcs is required to better understnd the trnsient phenomen, s the stedy-stte models do not provide the full picture. Some preliminry work in this re t Mintek hs lredy shown very promising results in using deterministic model of the rc to predict behviour tht strongly emultes the rel chotic movements of rcs. The dimeter to depth rtio of the rc depression hs been determined from photogrphs, nd this hs been used for electricl bth modelling. This pper is published by permission of Mintek. ACKNOWLEDGEMENT REFERENCES Bowmn, B., Jordn, G.R., nd Fitzgerld, F., The physics of high-current rcs, Journl of the Iron nd Steel Institute, June 1969, Bowmn, B., Properties of rcs in DC furnces, Electric Furnce Conference Proceedings,

9 Bowmn, B., 198. MHD effects in rc furnces, Symposium on Metllurgicl Applictions of Mgnetohydrodynmics. Bowmn, B., Effects on furnce rcs of submerging by slg, Ironmking nd Steelmking, No.. Jones, R.T., Brcz, N.A., nd Curr, T.R., Plsm Developments in Afric, Second Interntionl Plsm Symposium: World progress in plsm pplictions, EPRI (Electric Power Reserch Institute) CMP (Center for Mterils Production), Plo Alto, Cliforni, 9-11 Februry Mecker, H., Plsmstromungen in Lichtbögen infolge eigenmgnetische Kompression, Z. für Phys., Vol.141, (Quoted in Bowmn, B. Properties of rcs in DC furnces, Electric Furnce Conference Proceedings, 1994, ).

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