Scholas www.setscholas.og Knowledge is Powe June 2012 Volume 1, Issue 3 Aticle #07 IJASETR Reseach Pape ISSN: 1839-7239 Modeling of themal adiation in the intenal sections of a Thee-phase AC electical ac funace by means of a new tempeatue estimation method fo AC acs Abolfazl Nazai Depatment of Electical and Compute engineeing, Saveh banch, Islamic Azad Univesity, Saveh, Ian. * Coesponding autho s email: abolfazl.nazai@yahoo.com Abstact Wea and coosion has always had an advese effect on the pefomance and sevice life of electical ac funaces. Evey yea, lage amounts of money ae spent on eplacing the won out pats of these funaces which ae no longe usable because of coosion. One of the key causes of coosion in electical ac funaces is the themal adiation fom the acs. If the acs ae not popely coveed by slag, they will emit lage quantities of themal adiation into vaious intenal sections of the funace, which will lead to significant coosion in the wall and also the efactoy panels. The goal of this aticle is to estimate the amount of themal adiation which diffeent pats of the funace eceive fom the acs. In ode to calculate this heat, the tempeatue of the acs should be known. In this pape, a new method has been pesented fo the estimation of the AC ac tempeatues. The Bowman s model has been employed fo the simulation of the ac channel and the calculation of ac channel adius. The ac tempeatue has been estimated and used in a 3D themal adiation model; and the noted adiation model has been analyzed by linea Finite Element methods. Also, a linea method has been used fo the calculation of themal powe geneated by the acs. The biggest advantage of the poposed appoach is the simplification and eduction of complex calculations of themal and electomagnetic fields elated to the ac egion. The obtained esults show vey good coelation with the expeimental obsevations at the Isfahan Mobaakeh Steel Mills Complex. Keywods: AC acs, themal adiation, thee phase AC ac funace, and finite element methods. Citation: Nazai A. et al. (2012), Modeling of themal adiation in the intenal sections of a Thee-phase AC electical ac funace by means of a new tempeatue estimation method fo AC acs. IJASETR 1(3): p. 60-70. Received: 31-05-2012 Accepted: 09-06-2012 Copyight: @ 2012 Nazai A. et al. This is an open access aticle distibuted unde the tems of the Ceative Common Attibution 3.0 License. 1. Intoduction The electical ac funaces ae one of the biggest consumes of electicity. They convet electical enegy to themal enegy by utilizing high cuent acs. The themal enegy which is poduced in the acs is vey concentated, has a lage volume density and geneates a high tempeatue in them. Due to the high tempeatue of the acs, a lage potion of the heat tansfe between the funace s intenal sections is conducted though adiation. Diect themal adiation fom the acs to the efactoy mateials and also funace oof and wall panels damages them seiously. In the best case scenaio, these themal adiations esult in mino coosions. In the wost case, if the coosion occus in sections close to the molten 60
mateial, the funace could be punctued and molten mateials could seep out of the funace; this situation will be quite dangeous. In the altenating cuent AC acs, the acs don t have a fixed tempeatue [1], and the dimensions of the acs ae constantly changing [2]. Theefoe, if the facto of time and geometical changes of the acs ae taken into account, the exact analysis of the poblem of themal adiation fom the acs to the intenal funace sections becomes vey complicated and difficult to implement. Most of the eseach activities on the subject of themal analysis of ac funaces have only focused on the issue of themal adiation fom the ac to the bath [3, 4, and 5]. The subject of themal adiation fom the ac to the oof and walls and fom the bath to the oof has attacted less attention fom the eseaches [6, 12]. In [12], the effect of themal adiation fom the ac and molten pool to the funace oof was expeimentally investigated, and it was detemined that thee is no diect themal adiation fom the acs onto the oof. In [6], the themal enegy poduced in the acs unde nominal conditions has been calculated and then it has been assumed that 80% of this enegy is eleased as adiant heat in the intenal sections of the funace. In that aticle, the ac channel adius and its epeated changes have not been mentioned at all. Moeove, the manne by which the tempeatue of AC acs vaies is not identified. The assumption of 80% of themal enegy poduction in the acs being tuned into themal adiation has also been consideed by [9]. This assumption has been deived fom the esults obtained in [3]. The electical ac funaces (both the AC and DC types) have small efficiencies; and most of the geneated enegy in the acs is wasted in the fom of themal adiation into the intenal funace egions (except the potion which is absobed by the molten mateials). This enegy is usually collected and emoved fom the funace by the cooling wate lines that have been installed in the walls and oof. 2. Ac channel adius In this wok, the ac is modeled by the Bowman method as emanating fom a elatively small attachment aea on the gaphite electode in positive polaity mode and extends down to the suface of the molten bath. Eq. (1) descibes the shape of the conducting volume of the ac as a function of the distance fom the cathode attachment spot. An axisymmetic ac and no inteaction effects at the anode ae assumed, a k z 3.2 2.2exp( ) (1) 5 k In Eq. (1), the ac adius a, vaies with the distance z, measued fom the lowe suface of electode. The adius k is the cathode-spot attachment and is detemined by the instantaneous ac cuent. In Bowman model, cuent density in ac s A spot is appoximately constant ( J C 3500 [7]) and fo any defined cuent I in the electode, cm 2 k is: k I. (2) J C In each coss section of ac, ac s adius calculates fom Eq. (1). 61
Figue.1 shows these geometical dimensions. An AC ac in a positive polaity mode with positive cuent value at a time instant is vey simila to a DC ac with equal cuent. The shapes of the acs in AC electic ac funaces depend on the ac cuent and in addition ae vey sensitive to changes of imposed instantaneous voltage on seconday of the funace tansfome which causes the adius of the cathode-spot attachment to be changed. In AC acs, the cathode and anode change epeatedly in one cycle. In the positive mode the electode is the cathode and uppe suface of the molten metal bath is the anode and in the negative half polaity, this case is evesed. In the positive polaity mode, the ac ignition and the emission of electons take place at the lowest point of electode tip. In the negative polaity mode, ac initiation takes place at the uppe suface of molten metal bath. Theefoe, the emission of electons fom this suface is a complex phenomenon so that we have a vey complicated unstable ac [2]. In AC acs, the cathode-spot changes in popotion to the instantaneous cuent accoding to Eq. (1). This phenomenon is moe obvious fo high instantaneous cuents than low cuents. The ac geomety depends on the instantaneous cuent. Theefoe, it can appoximately give a schematic diagam of ac shape vaiations acoss the AC peiod fo an instantaneous polaity situation and fo ac geomety. Fig. 1: Bowman model fo DC ac Figue.2 depicts the instantaneous geomety of an abitay AC ac fo one peiod of AC cuent vaiations. As seen in Figue.2, the geomety of an AC ac depends on the value of instantaneous cuent. Change of cathode and anode can clealy be ealized in Figue.2. In any time, the smallest coss section of the cone is fo the cathode and the biggest coss section of the cone is fo the anode aea. Fig. 2: Schematic diagam of an abitay ac in a peiod of cuent wavefom [2] 62
The peceding discussion concludes that a pefect model of an AC ac, consideing its instantaneous geomety, would be vey complex to model in 3-D FEM. Theefoe analyzing such a model using the finite element method is complicated. In addition, a thee dimensional model, incopoating movable pats, should be simulated using tansient elements. Theefoe, it is useful to use a simple method fo the geomety of the ac. In this model, the movement of the ac is neglected. The AC ac is assumed to be a cylindical conducto with a time independent tempeatue. This model is simila to a DC channel ac model. If the existing hamonics in the ac cuent ae disegaded and the ac cuent is consideed as a completely sinusoidal one (elation (3)), then the ac will have, at evey height, a peiodic adius that vaies with time; and this adius will follow elation (4). I ac ( t) I sin(2 t / T) (3) m Since in the altenating-cuent (AC) acs, the diection of cuent changes at evey half-cycle, the cathode is displaced as well. Theefoe, elation (4) will have two sepaate pats coesponding to the two half-cycles. ( t, z) a z [3.2 2.2 exp( 5 k, )] max ( h z) [3.2 2.2 exp( )] 5 k, max ( k, ) max ( ) k, max 2 t T sin ( ) fo 0 t (4) T 2 2 t sin ( ) T fo T t T 2 k,max is the lagest possible adius of the cathode spot duing a peiod, and it is defined by elation (5): k max I m, (5) J C As is clea fom elation (4), the AC ac channel s coss section, at evey ac height, depends on z (distance fom the electode tip) and time. Thus, the tansient analysis of the themal adiation model is vey complex. The exact analysis of the tansient finite element will equie momentay values fo volume, mesh size and loading. In this eseach wok, steady state analysis has been caied out by using constant dimensions fo the ac and by consideing constant loading conditions. In this method, the ac channel adius has been calculated by aveaging the z and the time values ove the ac length and a time cycle, espectively. Relation (6) shows how the aveage adius of the ac channel is calculated. 0 h T 1 k,max h a ( z, t) dt dz ( ) 6.4h 22 k,max.[exp( ) 1] Th h 5 0 0 k,max Accoding to elation (6), the aveage adius of the AC ac only depends on the ac length and the peak of the sinusoidal cuent. The obtained esults fo 0 vesus the ac length and diffeent cuents (in RMS values) have been shown in Fig. 3. (6) 63
Having pefomed pecise measuements on electical acs, kohl was able to pesent a simple and linea model fo the AC electical acs. In his poposed model, ac esistance depends on ac length only and is expessed by elation (7). R ( 11.5h 0.1) m (7) In this elation, h denotes the ac length. Thus, by knowing the esistance and measuing the ac cuent, the themal powe poduced in the AC electical acs can be easily calculated. 3. Tempeatue distibution in the ac The objective of this section is to detemine the manne of tempeatue distibution ove the ac channel. In this section, it has been assumed that 80% of the geneated themal enegy in the acs is dispesed in the funace though adiation [3, 6, and 9]. The heat poduced in the acs has been estimated by the Kohl s linea model. Tempeatue at evey ac point has been consideed as a function of the distance of that point fom the ac channel axis. In this aticle, it has been assumed that the ac tempeatue has an exponential distibution with espect to the adial distance fom the ac channel axis. This assumption has been made based on the esults obtained in aticles cited in [1, 3, 4, 5, and 10]. Relation (8) shows this tempeatue distibution (in Kelvin). T( ) k e 2 k 10000, 0 (8) If the ac channel is assumed as a set of concentic cylindes having the same length and with adiuses smalle than 0, then the emitted themal adiation by each of these cylindes can be calculated fom elation (9) ( Q j is the emitted themal adiation by the j th cylinde with adius j ). Q j 4 T ( )(2 h) (9) j j The total amount of themal adiation fom the ac to the intenal funace sections will be equal to the sum of themal enegies emitted by this cylinde set. Thus, we will have: ( Q ad 4 T ( )(2 h) d 2 h T 0 0 Q ad denotes the total adiated enegy fom the ac). 0 0 4 ( ) d (10) As was peviously mentioned, it has been assumed that 80% of the poduced themal enegy in the acs is diffused in the funace as themal adiation. Theefoe, the main equation that elates the electical field to the themal field will be expessed as follows: ( Pac poduced by the electic field in the ac). Q 0. 8 ad P ac indicates the themal powe (11) 64
Qad will be calculated by elation (10) and Pac by the Kohl s elation. In ode to detemine the exponential distibution T(R), coefficients α and K should be known. Fo this pupose, besides using elation (11), the following bounday condition is also consideed. T( ) 10000 0 K (12) The pesented bounday condition in elation (12) indicates that the ac zone has been confined to a egion with tempeatues highe than 10000 degees Kelvin [1, 3, 4, 5, and 10]. Thus, coefficients α and K fo diffeent ac lengths and cuents ae calculated accoding to Figues (4) and (5), espectively. By having α and K coefficients, the tempeatue distibution ove the ac channel shall be detemined. The tempeatue distibution with espect to the adial distance fom the ac channel axis and fo diffeent cuents (in RMS values) has been shown in Fig. 6 fo a 30 cm AC ac. Fig. 4: k fo diffeent ac cuents (in RMS) in tem of ac length Fig. 5: fo diffeent ac cuents (in RMS) in tem of ac length 65
Fig.6: ac tempeatue distibutions in tem of adial distance fom ac axis (Ac length is 30cm) fo diffeent cuents 4. Themal adiation modeling The tempeatue of the adiating souce is the most impotant paamete in detemining the amount of themal adiation. Highe tempeatues poduce moe intense themal adiation fluxes. The themal adiation inside the electical ac funaces includes the themal adiation fom the acs and the eflected adiation by the oof and wall panels and by the molten mateial pool. The acs have high enegy volume density and theefoe thei tempeatue will be vey high. The volume density of the enegy poduced in the ac is diectly elated to the ac length and cuent. The themal adiation fom the acs can take thee outes inside the funace to get to the thee final destinations of wall, oof and molten mateials. Evey point on these thee outes will eceive a potion of the adiated enegy accoding to the point s distance fom the acs and also the view facto the point makes with the ac channels. The lagest amount of adiated enegy fom the acs gets to the molten mateials, because fist of all, the distance between them is vey shot and second, thee exists a good view facto between the acs and the pool of molten mateials. Themal adiation fom the acs to the walls and oof is pat of the enegy tansfe system s losses, and it diminishes the efficiency of the electical ac funaces. If the acs ae well coveed by slag, these losses will be educed. The amount of themal adiation fom the acs to the wall panels is much moe than that fom the acs to the oof. 5. Finite element modeling In ode to calculate the amount of themal adiation which is tansfeed fom the acs to diffeent inteio sections of the funace, a thee-dimensional model of a eal ac funace has been simulated in the ANSYS12.0 softwae. This funace, which is being used in the Isfahan Mobaakeh Steel Mills, is a 3-phase funace with the capacity of 200 tons. The simulated model includes the acs, oof and wall panels, molten pool and the efactoy. The mesh configuation of this funace has been shown in Fig. 7. Also, funace dimensions and physical specifications of diffeent sections of the funace, which have been used in the simulation, ae listed in Table (1). The 3D linea finite element analyses have been pefomed fo the steady state. The ac tempeatues have been detemined and used in the simulation accoding to the 66
appoaches pesented in the pevious sections. Also, the ac channel adius has been obtained by elation (6). It has been assumed that all of the mateials inside the pool ae molten and thei tempeatue is about 1800 degees Kelvin. Fo the pupose of isolating the simulation envionment fom the suounding space, a convection cuent with the tempeatue of 330 degees Kelvin has been consideed. All the inteio sufaces of the funace have been consideed as themal adiating sufaces with diffeent adiation coefficients. The geneal expessions of adiation heat tansfe using gay bodies diffuse adiation theoy fo an enclosed system of seveal adiating sufaces ae used [11]. The Radiation Matix Geneato is used to geneate a matix of view factos among adiating sufaces. This matix is theeafte ead as a supe element. In the inne egion of the funace only the themal tansfe by adiation has been consideed. Nomally duing the melting pocess, a majo pat of the efactoy mateials emains unde the molten mateials and anothe pat of it is coveed by the slag. When the slag has a small height o when thee is no slag at all, the themal adiation fom the ac to the efactoy intensifies and it will damage the efactoy mateials. Fig. 8 shows a tansvese view of tempeatue distibution in the funace bottom efactoy unde the nomal opeating conditions. Unde nomal woking conditions, the acs ae completely coveed by efactoy mateials (the height of the slag is about 50 cm). As can be seen in this Figue, the efactoy bicks which ae in the uppe sections (due to being next to the molten mateials) expeience a highe tempeatue. Table.1 Dimension and physical popety in the finite element modeling of AC thee-phase ac funace Input powe 68Mwatts Nominal phase cuent 80KA Appoximate dimension 4.5m 7.5m 8m Emissivity of ac 1 Emissivity of oof and wall 0.4 Emissivity of bath suface 0.6 Steel bath tempeatue 1800K Slag laye depth 0 and 0.5m Ac Length 30cm Fig. 9-a illustates tempeatue distibution in the efactoy fo when thee is no slag at all. In such a case, themal adiation fom the acs ceates thee hot zones on the efactoy mateials. The simulations show that when one of the acs gets close to the funace wall, the tempeatue of the closest hot egion to that ac inceases significantly, and this will lead to coosion in that hot egion. These cases occu when the ac banches out o when, because of the malfunction of the contol system, the ac deviates towad the funace wall. Since a long time ago, in the Mobaakeh Steel Mills, highe quality efactoy bicks (elative to the othe funace sections) have been installed in the thee noted hot zones. 67
Fig.7: meshing of thee-phase AC ac funace Fig.8: tempeatue distibution in the funace bottom efactoy unde the nomal opeating conditions (in Kelvin) The expeimental findings fom the field validate the simulation esults quite well. The tempeatue distibution in the wall panels fo the case in which the acs ae totally coveed by slag has been shown in Fig. 9-b. Because the lowe pats of the wall ae close to the acs, they will expeience highe tempeatues. Diect themal adiation fom the acs (when the slag height is zeo) causes seious damage to the wall panels. The effect of this diect themal adiation on the wall panels has been demonstated in Fig. 10-a. The tempeatue has dastically inceased in this Figue as compaed to Fig. 9-b. Fig.9: a) Tempeatue distibution in the efactoy fo when thee is no slag at all (in Kelvin) b) Tempeatue distibution in the wall panels fo the case in which the acs ae totally coveed by slag (in Kelvin) Fig. 10-b shows the tempeatue distibution in the exteio sufaces of the funace fo the case in which thee is no slag at all. Tempeatue in this case also inceases in the exteio egions of the funace; and those exteio sections that ae 68
located whee the funace nose joins the funace wall will expeience a highe tempeatue incease. The themal adiation fom the acs has no effect on the tempeatue of funace oof [12]. The eflected adiation fom the molten mateial pool aises the tempeatue of the acs. The funace oof has an almost adial tempeatue distibution patten, and its cental egions have highe tempeatues. The tempeatue distibution on the oof has been illustated in Fig. 11. Fig.10:a) Tempeatue distibution in the wall panels fo when thee is no slag at all (in Kelvin) b) Tempeatue distibution in the exteio sufaces of the funace fo the case in which thee is no slag at all (in Kelvin) 6. Conclusion Fig. 11: tempeatue in the oof (in Kelvin) In this aticle, a linea electical model has been used fo the AC acs. A new method has been poposed fo the calculation of the ac channel adius and tempeatue distibution on the ac channel. 3D finite element methods have been employed fo the estimation of themal adiation eceived by diffeent pats of the funace. In the 3D simulation, the eal 69
dimensions of a 200-ton funace, including the acs, bath, efactoy panels and also wall and oof panels, have been used. In this model, the acs act as the souces of themal adiation; and the themal adiation fom the ac is eceived by the wall panels and by the bath and efactoy. The themal adiation fom the acs to the efactoy unde the no-slag conditions ceates thee hot egions on the efactoy. The hot zones obtained in the simulations confomed to the damagepone egions of the efactoy panels that had been discoveed in the Mobaakeh steel mills funaces. Since a long time ago, these egions ae being coveed with highe quality bicks compaed to the othe funace sections. Pats of the wall panels that ae next to the acs always expeience highe tempeatues. The themal adiation fom the acs to the oof has no effect on the oof tempeatue (due to ineffective view facto and long distance between the acs and the oof). This pape pesents a simple and accuate calculation method fo the analysis of themal adiation in the inteio sections of altenating-cuent (AC) electical ac funaces. In this appoach, by having the ac length and cuent, the ac channel adius and tempeatue ae easily detemined. Using the acs with known tempeatues in a 3D finite element analysis, the amount of themal adiation fom the acs to diffeent intenal sections of the ac funace can be obtained. Refeences [1] J.A.Bakken, L. Lasen, and V.G.Sevastyanenko, Numeical modeling of electic acs, Jounal of Engineeing Physics and Themophysics, Vol. 70, No. 4, 1997. [2] A.Kiyoumasi, A.Nazai, M.Ataei, H. K.Beheshti, and R, Hoshnand, Electomagnetic analysis of an AC electic ac funace including the modeling of AC ac, Compel, Vol.29, No.3, pp.667-585, 2010. [3] J.Alexis, M.Ramiez, G.Tapaga, and P.Jonson, Modeling of a DC Ac Funace- Heat Tansfe fom the Ac, Ion steel Inst Jpn, Vol.40, No.11, pp. 1089-1097, 2000. [4] F. Qian, B. Faouk, and R. Muthaasan, Modeling of fluid flow and heat tansfe in the plasma egion of the dc electic ac funace, Metallugical and Mateials Tansactions B, vol.26b, pp.1057-1067, Octobe 1995. [5] M. A. Ramiez, Mathematical modeling of DC electic ac funace opeations, Massachusetts Institute of Technology, Ph.D. Thesis, Septembe, 2000. [6] G. Diancai, and A. Ions, Modeling of adiation intensity in an EAF, thid intenational confeence on CFD in the mineal and pocess industies CSIRO, Melboune, Austalia, 2003. [7] R. T. Jones, Q. G. Reynolds, and M. J. Alpot, DC ac photogaphy and modeling, PERGAMON, Mineals Engineeing, Vol.15, pp.985-991, 2002. [8] P. P. Pavia, Modeling and contol of an electic ac funace, Maste Thesis, Depatment of Automatic Contol, Lund Institute of Technology, June 1996. [9] F. David, T. Tudoache, and V. Fitean, Numeical evaluation of electomagnetic field effects in electic ac funaces, Compel, Vol.20, pp.619-635, 2001. [10] M. Ramiez, and G.Tapaga, Mathematical modeling of a DC electic ac dimensionless epesentation of a DC ac, Ion steel Inst Jpn, Vol. 43, No.8, pp. 1168-1176, 2003. [11] R. Siegal and J. R. Howell Themal Radiation Heat Tansfe,3 d ed, Hemisphee Publishing Copoation, Washington,DC, 1992. [12] Q. Reynolds, Themal adiation modeling of DC smelting funace feeboads, Mineals Engineeing, vol.15, pp.993-1000, 2002. 70