MODELING OF RADIATION INTENSITY IN AN EAF

Transcription

1 Thrd Internatonal Conference on CFD n the Mnerals and Process Industres CSIRO, Melbourne, Australa December 2003 MODELING OF RADIATION INTENSITY IN AN EAF Danca GUO and Gordon A. IRONS Steel Research Centre, McMaster Unversty Hamlton, Ontaro, Canada L8S 4L7 ABSTRACT To understand the meltng process of steel scrap n an Electrc Arc Furnace (EAF), a radaton model has been developed to quantfy the radant energy dstrbuton nsde the furnace. Usng the operatonal voltage, current, and power factor, the energy radated from an arc s determned. Radaton laws are cast nto a dscretzed form to compute the energy ntensty nsde the furnace. Ths model enables the separaton of the energy receved by a surface nto the part from each arc and that from the bath surface. The effect of arc length and slag foam heght s examned. The energy dstrbutons on sdewall refractory, water-cooled sde panels and furnace roof are obtaned. Model predctons are n good agreement wth ndustral observatons. The porton of arc energy gong nto an electrode s examned n detal, and t s found that the value suggested n some publcatons s too hgh for modern furnace practce. NOMENCLATURE A: coeffcent nb: neghbor a: area q: heat source Cp: specfc heat R,r: resstance / radus e: energy S: total source term F: vew factor T,t: temperature / tme G: rradaton ε: emssvty I: electrc current ρ: densty J: radosty Γ: heat conductvty INTRODUCTION Electrc furnace steelmakng has captured almost half of the world s steel producton. Despte ts mportance, relatvely few studes have been carred out to nvestgate the transport phenomena assocated wth scrap meltng. The present work, on radaton from the arcs, s part of a larger program to nvestgate the entre process. Other work addresses heatng from oxy-fuel burners, scrap movement, meltng n the lqud bath and postcombuston. RADIATION MODEL Most EAFs operate wth 3 graphte electrodes n 3-phase AC at 100 to 400 V and up to 100 MW on the secondary sde of a furnace transformer. Measurements are usually made on the prmary sde of the transformer, ncludng a reactor. The power to the arc s less due to losses n the reactor, n the furnace transformer, and n the bus bar and cables of the secondary crcut. When the electrcal resstance and reactance of each of the above-mentoned components are known, the electrc resstance of the arc column under a specfc operatng condton can be obtaned. Once the amount of energy released from an arc s known, the energy radated from the arc s smply that mnus the part drectly delvered to the metal bath or scrap n the arc mpngement zone, and the part absorbed by the graphte electrode. The estmaton of Alexs et al (2000) that 18% of the energy release from an arc s drectly delvered to the metal bath, has been adopted. It s assumed that 2% of the energy released from an arc absorbed by the electrode. Ths assumpton wll be addressed at the end of ths paper. From these assumptons, 80% of the energy released from an arc s delvered n the form of radaton; the surroundng slag layer wll ntercept part of t. The radaton model wll determne the dstrbuton of the remander nsde the furnace. Whle there are models to compute the temperature of a DC arc (eg. Alexs et al. (2000)), AC arcs are more complex n that they fluctuate over the cycle, are deflected and precess due to arc nteractons and, furthermore, the pont of arc attachment moves over the electrode surface. Gu and Irons (1998) employed a channel arc model that showed that the arc could be approxmated by a cylnder, or a cone of small concal angle. Therefore, t s assumed that the radatng surface can be well represented by the extended surface of a cylndrcal electrode, but deflected outwards from the furnace center. Gven the arc length and the amount of radated energy, the energy flux from ths radatng surface s known. Ths surface s subsequently dvded nto 72 x 20 (crcumference x heght) elements, each acts as a black body n radatng, but perfectly transparent n recevng. The movement of the arc s neglected. Furthermore, gas radaton and partcle absorpton are neglected. Assumng that the nner surface of the furnace, as well as the top surface of slag or steel, behave as gray body surfaces, for any small area a, ts radosty J,.e. the energy leavng the area, rradaton G,.e. the ncdent radant energy, and emssvty ε, are related by (Karlekar and Desmond, (1977)): J = (1 ε ) G + ε e (1) Here the rradaton ncludes the ncdent radaton from all radaton sources, such as arcs, bath surface, and walls: b Copyrght 2003 CSIRO Australa 223

2 1 n 1 G = Σ a jfj J j (2) a j= 1 n s the total number of small areas consdered, and F j- s the vew factor between surface a j and a. As the term e b s related to the temperature of a, the net energy ganed through radaton can be treated as a source n the energy conservaton equaton of all control volumes consdered. An teratve method s used to fnd all G, and hence J, leadng to the soluton of temperature of the nner surfaces of the panels and roof, the refractory surface, as well as the nteror of the refractory wall, based on the SIMPLE scheme (Patankar (1980)),. For these control volumes (CV) the energy, or enthalpy conservaton, s gven as: ( ρcp T) ( Γ T) = q t n whch q s the heat source, ncludng that exchanged by convecton and radaton, and the latter s: q (3) = G J (4) A code based on prevous modelng work on flow and mass transfer (Guo and Irons (2000)), updated wth nonorthogonal control volumes, was used to carry out these calculatons, and to solve the energy conservaton equaton. One feature of the code s that most varables are treated as vectors, such as radaton fluxes, dstances, surfaces (wth areas projected to the coordnate planes as components). The radaton from one surface to another can be obtaned by smple dot multplcaton. The calculaton of the angles between a surface normal and varous connectng lnes s thus avoded. The calculaton proceeds as follows. The value of the G functon for the furnace nternal surface of each related CV s obtaned by accumulatng the radaton from all other CVs surface, as shown by Equaton (2), and that of J functon by Equaton (1). These values gves q, whch s then used n Equaton (3) to calculate the temperature of each CV at the next tme step. Ths procedure s repeated to update G and J, untl the total relatve error, ( A nbtnb + Sp A ptp ) Tp, s smaller than 10 3 for the whole doman (nb means all neghbor CVs). Then next tme step starts. As a check, the code s used to calculate the radaton from the bath surface of a cylndrcal furnace, receved by the parallel planes n the freeboard. By settng the bath surface as an deal emtter, and all the other parts as black bodes at zero temperature, the rato between the energy receved by these planes and the total emtted energy should be equal to the vew factor. The calculated results are presented n Fgure 1, and compared wth analytcal solutons publshed n the lterature (Karlekar and Desmond, (1977)). It can be seen that the accuracy of the code s satsfactory. An ndustral furnace s meshed as shown n Fgure 2. Electrode 3 s on the left closest to the slag door where slag overflows. The furnace s tapped through a taphole on the other sde of the furnace bottom. Basc Vew Factor F W.H. McAdams Radaton Model Rato d/x Fgure 1: Calculated vew factor by the model assumptons and nput values for smulatons are summarzed n Table 1. Fgure 2 Industral furnace meshng, tappng sde at rght. Modelng Results Fgure 3 gves the radaton ntensty from arcs on the sdewalls, ncludng the refractory (mmedately above the bath), water-cooled panels (hgher n the freeboard) and the vertcal part of the roof, flattened for presentaton. The frst contour lne from the bottom corresponds to the part of water panels, showng the effect of electrode proxmty. Below ths lne, the part of hgh ntensty corresponds to the refractory wall, as t s closer to the arcs. The contour shape of ths zone s due to the rregular shape of the steel bath, and the walls around the slag door (fgure centre) Earc, Kw / M2 Fgure 3: Arc radaton ntensty on the sdewalls, H slag =0, L arc =557 mm, P act. =94.8 MW

3 Table 1: Basc assumptons for numercal smulatons Steel bath depth: 1.26m Slag layer depth: 0.0, 0.1, 0.2, 0.3, 0.4 m Exposed refractory heght: 0.4, 0.3, 0.2, 0.1, 0.0 m Steel bath temperature: 1500, 1550, 1600 C Slag top layer temperature: 1600, 1650 C Smulated tme perod: 2.5 hours to reach the quas steady state* Convecton coeffcent for coolng water 10.0 kw/m 2 K Convecton coeffcent for ambent ar 2.4, 5, 6 W/m 2 K for bottom, wall and roof Thckness of panel & roof slag coatng 20 mm Heat conductvty of slag coatng 2.2 W/m K Heat conductvty of refractory 2.4 W/m K Heat conductvty of nsulaton layer 0.1 W/m K Dstance from slag top to electrodes 52 to 557 mm Actve power nput rate 83.5, 90, 93.6, 94.8 MW *to be explaned n the followng Fgure 4 shows the radaton from the steel bath to the sdewalls. The tappng sde refractory, beng more vertcal, receves more radaton than the slag door sde (mddle of fgure). The radaton ntensty from the bath s much lower than that from the arcs, about one thrd n ths case. Earc, Kw / M2 Fgure 4 Intensty of radaton from bath surface on the walls, H slag =0, T steel =1500 C Fgure 5 shows the arc radaton on the steel bath surface. The center regon receves the most ntense radaton, n the range of about 10 MW/m 2. Ths ntensty means that a 2-mm thck steel sheet, wth an emssvty of 0.5, wll be melted wthn 1 second solely by radaton Earc, Kw / M Fgure 5 Arc radaton ntensty on bath surface, H slag =0, L arc =557 mm, P act. =94.8 MW. The model enables calculaton of radant heat exchange nsde an EAF, heat flux calculatons, estmatons of the hot-face temperature of the slag coatng on the watercooled panels and roof, and so on. Due to the fact that the hot-face temperatures of water-cooled panels and roof, and the temperature dstrbuton n the refractory wall, are not known a pror, a transent process was adopted to approach a quas-steady state for radaton heat exchange. A guessed hot-face temperature dstrbuton for fxed slag and steel temperatures s used to compute the fluxes, and update the temperatures. In ths way, the temperatures of refractory, panels and roof gradually approaches a quassteady state value. As radaton nvolves the fourth power of temperature, drectly smulatng a steady state s not practcal, due to poor convergence, and the need of extremely heavy under-relaxaton. Fgure 6 shows the progress of temperature and rradaton for a montor CV for one case, ndcatng that ths method ndeed leads to a quas steady state. Temperature montorred, o C Smulated Tme, s Fgure 6 Smulated temperature and rradaton varaton of a montor CV H slag =0.3 m, P act. =93.6 MW, L arc =521 mm. Fgure 7 shows the hot-face temperatures for an exposed arc length of 257 mm. The temperatures are relatvely hgh, refractory hot face above 1700 C. The protectve slag coatng on the panels start to melt at temperatures of about 1400 C Irradaton Montorred, kw/m 2 225

4 T, C Fgure 7 Calculated EAF nner temperature, H slag =0.3 m, T slag =1600 C L arc total =557 mm, P act. =94.8 MW All modern EAFs use a foamy slag practce n whch carbon monoxde s delberately evolved to foam up the slag, and bury the arc n the slag. The objectves are to reduce heat losses, refractory eroson and electrcal and acoustc nose. Fgure 8 shows the effect of varyng slag depth on radatve heat exchange for a fxed total arc length of 452 mm. Both the sde panels and roof are water cooled, so the heat extracted by coolng water s the sum of those two quanttes. The heat absorbed by slag surface and by sde panels are most strongly affected by exposed arc length. Under the smulated condtons, the net gan by slag surface becomes negatve, as the exposed arc length s less than150 mm, whch s the normal operatng condton. For the prototype furnace on whch these calculatons were based, the heat extracted by coolng water vares between 17 and 22 MW n the refnng perod, whle the smulated values are between 12 and 15 MW. Consderng that the addtonal convectve heat from the exhaust gas s estmated to be 3 to 6 MW for ths perod, the agreement s very good. Heat Absorbed, MW Heat extracted by coolng water By sde panels By roof By refractory wall L arc = m. Normal Operatng Range By slag top surface Slag Depth, m. Fgure 8 Effect of varyng slag depth on radaton heat exchange ENERGY ABSORBED BY AN ELECTRODE FROM ARC It has been estmated that about 14% of the total energy released from an arc s dsspated n the electrode (Jordan et al (1985), and Amelng et al (1986)); however, t s expermentally dffcult to verfy ths fgure. The followng calculaton places an upper bound on ths quantty wth a smplfed steady-state heat transfer calculaton. Assumng that an electrode s workng at a steady state, the heat flowng nto the electrode from the hot tp, plus the Joule heat generated n the electrode, s balanced by the heat conducted out from the cold end, and that radated to the surroundng. Therefore, when the temperature dstrbuton of an electrode s known, these heat transfer terms can be easly calculated. The problem can be convenently solved as a twodmensonal heat flow problem wth non-sotropc, but constant, heat conductvty and electrc resstvty. The cylndrcal electrode s dvded nto small control volumes, wth fner ones near the hot tp and the outer surface. The heat transfer n an electrode s governed by equaton (3), wth the addtonal source term for joule heatng: q = I 2 R The electrcal current densty, due to the skn effect, s determned by: I I 0 r 0.234( ) r (5) 4 = + (6) for an electrode of 610 mm dameter, Orth (1985). The proxmty effect of other electrodes s not consdered, wth I 0 the nomnal current densty. The physcal propertes of an electrode and boundary condtons for equaton (3) are lsted n Table 2. The sublmaton temperature of graphte electrode s about 3925 K, and above 3000 K the electrode deterorates rapdly (Touloukan (1970)). Hot-tp temperatures between 2000 and 3600 K were examned n the calculaton. The computaton was accomplshed wth the smple code mentoned earler (Guo and Irons (2000)). Table 2 Physcal propertes of electrode and Boundary condtons Electrode Dameter 610 mm Electrode Length 4 m Electrcal specfc resstance, 5.2 Ohm.mm 2 /m longtudnal * Thermal conductvty 230 W/m K * coeffcent, longtudnal Thermal conductvty 150 W/m K * coeffcent, radal AC Current Amperes Hot tp temperature K, 400 K nterval Cold tp temperature 400 K Emssvty of graphte 0.85 Surroundng temperature 400 K * (Klen et al. (1995)) The calculated temperature dstrbuton for one case s shown n Fgure 9. In Fgure 10 the surface and centre temperatures of the electrode for the 2 hot-tp temperatures s plotted, showng that most of the temperature varaton occurs at the ends, and that beyond 1 meter from the hot tp the temperature stays almost the same for dfferent cases

5 T, K Fgure 9 Temperature dstrbuton n an electrode D=610 mm, I=61500 Amp, T 0 =3600 K, T amb.=400 K. Temperature, o K = 3600 o K, Centre = 3600 o K, Surface = 2000 o K, Centre = 2000 o K, Surface Dstance from Hot Tp, m. Fgure 10: Electrode surface and center temperature D=610 mm, I=61500 Amp, T amb.=400 K. To provde a closer estmate of the losses n the electrode there are two quanttes n the model to be more precsely defned: the hot-tp temperature and dameter. Examnatons of publshed vdeo recordngs of arcs suggest that the hot tp of an electrode (excludng the arcng spot) s usually darker than the steel bath (Jones (1998)). The arcng spot area s small compared to the tp area, whch s smaller than the electrode secton due to penclng. Therefore, a hot-tp temperature of 2400 K seems more reasonable, leadng to 2% loss, used n the radaton model earler. Of course, ths value needs to be verfed expermentally, but t seems much more realstc than 14%. CONCLUSIONS A radaton model has been developed to quantfy the radatve energy exchange nsde an EAF, whch enables the separaton of radaton from dfferent sources, and the determnaton of heat extracted by water-cooled panels and roof. It also permts the estmaton of the effect of exposed arc length, and hence the slag foamng heght, on the refractory walls, and determnes the temperature dstrbuton of dfferent parts of the furnace. Calculated energy radated to water panels and roof s n good agreement wth observed values, ndcatng that the model can be used as a valuable tool n evaluaton of EAF furnace desgn and operatonal parameter optmzaton. Heat transfer analyss of a graphte electrode reveals that wth an average hot tp temperature of 3600 K, that no more than 5.5% of the electrc energy s absorbed from arc by the electrode at steady state. It s argued that 2400 K s a more reasonable temperature, resultng n a loss of 2%. The heat loss by conducton through an electrode s about 0.3% of the total electrc energy for the smulated cases. Ths value s much less than the Joule heat produced nsde the electrode (1 to 1.5%). Q / Total Electrc Energy, % Joule Heat Qout Qn, =3600 K Qn, =3200 K Qn, =2800 K Qn, =2400 K Qn, =2000 K Furnace Total Actve Power, MW Fgure 11: Percentages of exchanged heat over total electrc energy D=610mm, I =61500 Amp, T amb.=400 K. The heat transfer terms assocated wth the electrode are compared wth the electrc power nput n Fgure 11. It s clear that the maxmum heat flowng nto the 3 electrodes from the hot tp, Q n, s less than 5.5% of the total electrc energy. Also note that the heat flowng out of the electrode from the cold ends, Q out, s only about 0.2 to 0.3% of the total electrc energy under the gven condtons, and the Joule heat generated n the electrode s 1 to 1.5%. REFERENCES ALEXIS, J., et al, Modelng of a DC electrc arc furnace-heat transfer from the arc, ISIJ Internatonal, Vol. 40, 2000, pp GU, L.P. and IRONS, G.A., 1998, Physcal and Mathematcal Modelng of Flud Flow n Electrc Arc Furnaces, Electrc Furnace Conference Proceedngs, vol. 56, Iron and Steel Socety of AIME, New Orleans, Nov , pp JONES, R., Prvate communcaton, 1998, Mntek, South Afrca. KARLEKAR, B.V. and DESMOND, R.M., ENGINEERING Heat Transfer, West Publshng Company, New York, 1977, p.240. PATANKAR, S., Numercal heat transfer and flud flow, Hemsphere Publshng Corporaton, 1980, New York, p GUO, D. and IRONS, G., Modelng of Gas-Lqud reactons n Ladle Metallurgy: Part II. Numercal Smulaton, Metal. & Matls. Transactons, B 31, P.1457, JORDAN, G.R., et al, Basc propertes of hgh ntensty electrc ARCS used n steel makng, Brtsh Steel Corporaton, ECSC Conventon, No /9/801; cted from E. Ploecknger and O. Etterch, Electrc 227

6 Furnace Steel Producton, Englsh Translaton, John Wley and Sons, Chchester, 1985, p.131. AMELING, D., et al, Untersuchungen zur Schaumschlacken m Electrolchtbogenofen, Stahl und Esen, 106 (1986), Nr.11, pp ORTH, G., Current dsplacement n graphte electrodes for arc furnaces (German), Electrowaerme, B 34, 1976, pp.25-30, cted from E. Ploecknger and O. Etterch, Electrc Furnace Steel Producton, Englsh Translaton, John Wley and Sons, Chchester, 1985, p.130. TOULOUKIAN, Y.S., et. al, Thermophyscal PROPERTIES of Matter, IFI/Plenum Publcaton, New York, 1970, Vol. 2, p.23. KLEIN, R.D., et al, DC electrodes-a key factor for progress n EAF steel producton, Metallurgcal Plant and Technology, Vol. 18, 1995, p