Modelling Vortex Fields in Metal Smelting Furnaces

Transcription

1 Int. Jnl. of Multiphysics Volume 4 Numbe Modelling Votex Fields in Metal Smelting Funaces Oleg Kazak, Oleksand Semko Depatment Of Physics, Donetsk National Univesity, Donetsk, Ukaine olegkazak@yandex.u; semkoan@dongu.donetsk.ua ABSTRACT The pesent wok is devoted to studying of electovotical movements of the liquid metal in electic funaces. The statement of a poblem, physical and mathematical model of poceeding pocesses ae given. The algoithm of the poblem solution is developed and the esult of electomagnetic fields in liquid metal executed by pogammatic-calculable complex ANSYS is eceived. Keywods: Loentz foce, modelling, electovotex movement. INTRODUCTION Diect-cuent electic funaces with a bottom electode have ecently become vey popula in metallugy [ 3]. Such funaces ae moe pofitable and envionmentally fiendly. Typical cicuit fo such a funace and its pinciple paametes ae given in Fig. []. The pinciple elements of the funace ae: a body with the lining backing, a smelting bath, top and bottom electodes. The funace opeation showed the inceased wea at the bottom electode. The eason fo inceased wea is supposed to lie in votex cuents of liquid metal caused by the Loenz foce [4]. Votex cuent of liquid metal comes up because of spatial homogeneity of cuent density and electic-magnetic field. Theefoe, the most impotant objective is to estimate the Loenz foce intensity, the affect of diffeent factos on the Loenz foce and the votex movement chaacte of the molten metal. Smelting metal in electic funaces epesents an extemely complex, enegy consuming and expensive physical pocess that flows at high tempeatue, is accompanied by poweful electic and magnetic fields, intensive liquid metal votex movements. These conditions make theoetical and expeimental eseach much moe complicated. That is why moden numeical methods and physical models of electic steel-smelting funaces fo numeical modelling have been widely used in metallugy. Fundamental laws lying in the basis of the calculations make it possible to detemine the stategic line of impoving the technology no matte what occasional factos can come up in the eal poduction pocess. Calculation of the pocesses in electic funaces equies taking into account electomagnetic, themal, stength and hydodynamic phenomena and poses geat demands to the means of numeic modelling.. PHYSICAL PROCESSES IN ELECTRIC FURNACES FOR SMELTING METAL To descibe physical pocesses in the funace let us have a look at the electic diect-cuent steel-smelting funace with symmetical electodes and axisymmetic bath, which is filled with liquid metal and is woking in the steady-state mode. In Fig. the typical configuation of the DC steel-smelting funace with the axisymmetic bottom electode is given. The main pats of the configuation ae - fettle, -liquid metal, 3-top and bottom electodes.

2 35 Modelling Votex Fields in Metal Smelting Funaces Funace capacity m 00 T Diamete of funaces D 5500 MM Depth of bath h with melted steel 00 MM Diect cuent Cuent load I κa The mainlines voltage is U B Powe of cuent consumption N MBT Polaity «+» on bottom electode Electode diamete d 500 MM Lining thickness h f 650 MM Specific conductance of lining σ f (Ω M) Specific conductance of liquid metal σ 0, (Ω M). Figue Industial DC ac funace with bottom electode. Figue Model of physics pocess in DC ac funace. The DC potential is applied to the electodes, positive voltage to the bottom electode, and negative to the top one. Unde the impact of the voltage given to the electodes, the cuent is found in the molten metal. The cuent lines maked with symbol j in Fig. lie in axial sections. Fom the Ampee s cicuital law fo any coss section of the funace I = jds = const, if S is the coss section aea of the heath of the funace at a cetain level, S and cuent line path, it follows that the futhe it is fom the symmety axis the lowe cuent density is. This cuent geneates axisymmetic magnetic field with magnetic inductive vecto lying in the plane pependicula to the symmety axis, i.e. in the hoizontal plane. Magnetic paths (maked with the B symbol) ae concentic cicles, pependicula to the symmety axis. The cuent conducto in the magnetic field is affected by the Ampee foce with the volume density of fe. This foce is pependicula to the cuent density and magnetic = j, B j induction B. Fo the scheme in question the f e foce is diected towads the symmety axis and lies in the axial plane. It has two components: adial and axial. The adial component is diected towads the symmety axis, while the axial one is diected at the opposite electode. The adial component causes coss-compession of the conducto, so-called pinch-effect.

3 Int. Jnl. of Multiphysics Volume 4 Numbe This foce affects the singled out element of the liquid conducto with the linea o olling motion. Unde the influence of this foce the element moves as a whole towads the symmety axis and otates in the diection of the symmety axis. But the conducto being liquid, the votex flow appeas. The necessay condition fo the votex flow ( ) to appea is the votex natue of the electomagnetic foce ( ot ot v 0 f e f e 0). Such a type of the flow appeas if the cuent is spatially uneven. In this example the votex flow of liquid metal is the esult of spatial unevenness of the cuent with the absence of oute magnetic field. The cuent in the liquid ceates a magnetic field of its own, which causes votex movement of the liquid. 3. MATHEMATICAL STATEMENT OF THE PROBLEM To build a mathematical model of the pocesses in electic steel smelting funace let us take the following assumptions. the medium is consideed non-magnetic; the medium is a good conducto and its pemittivity can be ignoed; convective cuent, caused by the medium movements compaed to the cuent of conductance can be ignoed; heat convection may be caused by the uneven Joule heating and is taken into account by the dependence of the medium density on the tempeatue and pessue by the given law ρ= ρ( p, T) ; medium heating caused by viscosity (viscous dissipation of enegy) can be ignoed as compaed to the Joule heating; chemical eactions ae not taken into account. The pocesses flowing in the electic funace duing metal smelting ae not steady. Howeve, they ae athe slow and can be descibed in quasi steady o just steady fomulation. Fo steady pocesses the system of equations of magnetic hydodynamics, descibing the movement of the molten metal in the funace is as follows [4 5]: momentum equation v v p ν v g j, B ρ ρ ( ) = heat tansfe equation () ρcv T χ T ( ) = + j ; σ () equation of continuity ( ρv ) = 0; (3) Maxwell s equations B = 0;, H = j;, E = 0; D = ρe; coupling equation (constitutive equation and Ohm s law fo fluid in motion) D= 0E, B= 0H, j = E+ v, B ; εε µµ σ ( ) (4) (5)

4 354 Modelling Votex Fields in Metal Smelting Funaces chage consevation law j = 0; (6) whee: v liquid velocity, ρ density, p pessue, g acceleation of gavity, ν coefficient of kinematical viscosity, j cuent density, B field density, T absolute tempeatue, c specific heat of media, χ heat conduction coefficient, σ specific conductance, ε 0 µ 0 electical and magnetic constant, E dielectic field intensity, ρ e volume density of electic chage. Following foces ae consideed in equation (): pessue foce, foce of viscous dag, gavitation, ρ ν ρ p v g j, B Loenz electomagnetic foce. The equations given below expess consevation laws of enegy at tansition though an inteface of medium: fo electic field E = E, D D = ρ ; n n n n e fo magnetic field B = B, n B= n B n+ B τ B ; ( ) = = n n n τ τ 0 (7) (8) fo cuent density on bounday with insulated and nomal coss-section of electode j =, j = j = I S. n 0 n 0 (9) On the lines of the aea calculated atificial non-eflective bounday conditions [6]. 4. METHODS OF SOLUTION The poblem in question has no analytical solution and theefoe it was solved numeically. As a esult of the analysis of the numeical methods of solution the method of finite elements [7] and ANSYS system [8] wee chosen. The poblem belongs to the class of conjugate and the stategy of solution consists of the following stages: st stage solving electomagnetic fields; nd stage solving electovotex flows; 3 d stage solving electovotex flows with the account of heat exchange and convection. Such ode is accounted fo by the equiements to consequent conjugant analysis in ANSYS system [8 9]. The main idea of this analysis consists in joining two sphees (disciplines) by imposing the esults of the solution of each stage as the loads fo the following stage of the analysis. The esults of the electomagnetic poblem ae the values of the components on X, Y, Z axes, electomagnetic foce and magnetic flow density, found in each nodal point of the calculated aea. Using these stages esults, it is possible to calculate the components of smelting motions ( nd stage) caused by electomagnetic impact. Moeove, the esult of the st stage is the amount of heat pe the unit of volume got in evey nodal point. The value of this heat can be used as initial data fo heat exchange poblem solution (3 d stage), which is the distibution of flow velocity. Afte that the found values of the tempeatue in evey nodal point, as well as liquid metal velocity ae specified taking into account heat exchange, convection and conditions of heat change on the boundaies of the calculated aea and, as a esult of this, we can do the calculation of the hydodynamic poblem.

5 Int. Jnl. of Multiphysics Volume 4 Numbe MODELLING PROCESSES IN ELECTRIC FURNACES Now let us have a look at the test poblem of calculating electic and magnetic fields fo axisymmetic volumetic conducto in the fom of a cylinde that maximally coespond to industial funace (Fig 3). The calculated aea by axial symmety of the poblem makes half the eal aea. and ae electodes, 3 is fo ion cylinde, 4 is fo medium (ai). The initial data ae as follows: cuent load I = 80 κa, specific conductance of liquid metal σ = 0,9 0 6 (Ω M), specific conductance of electode σ = 0, 0 6 (Ω M), elative pemeability of liquid metal and electode µ =, elative pemeability of media µ =, elative capacitive of media ε =. The calculations wee made at the following bounday conditions: the cuent density on the electode ends is given, o values of the potentials, coesponding to the initial cuent density; the conditions of continuity of the standad component objects on the side sufaces of the electodes and cylinde ae given; the conditions of continuation of the fields and infinity conditions ae given; on the symmety axis of the calculated aea the conditions of axial symmety ae given. The calculations wee done by using diffeent analyses at diffeent schemes. It was found out that the esults of the calculations had been consideably influenced by the size of the calculation mesh and by finite esults. The peliminay analysis showed it is optimal to divide them into elements, as well as to shape them in quadangula fom with fou nodes. The domain was split into elements unevenly: in the aea of the bottom electode, whee lage gadients of electomagnetic paametes, elements wee densely located and wee of small size. The othe pats of the domain whee gadients of the paametes ae not that significant the elements wee located not so densely and wee of lage size. The effect of the bounday conditions on the atificial boundaies of the domain on the paametes in the cental zone was investigated. It was found out that the esults of bounday conditions changes ae not significant in compaison with non-eflecting bounday conditions, and makes up about 0.7%. In Fig. 4 demonstated the vecto and outline fields of the Loenz foce nea the bottom electode (anode). The esults of the calculations pove the fact that the Loenz foce in such funaces is detemining if electo votex flow appea. The given esults ae well-coelated with the expeimental data (inceased fettle wea). Simila calculations wee done in the COMSOL system. The esults of calculations in ANSYS wee compaed with the esults of calculations in COMSOL. The coinciding esults of calculations by diffeent methods and packets (Fig. 4) pove eliability of the models, methods and significance of the esults. Figue 3 Model of industial DC ac funace.

6 356 Modelling Votex Fields in Metal Smelting Funaces Suface: sqt(jz_emgh.^+j_emgh.^)*bphi_emgh (N/M3) Contou: sqt(jz_emgh.^)*bphi_emgh (N/M3) Aow: (-Jz_emgh.*Bphi_emgh, J_emgh*Bphi_emgh (N/M3) Max: 3.307e4 Max: 3.0e4 x04 x Liquid ion xoxoxoxoxxxox xoxoxoxx xoxoxoxx 0.5 Electode Insulato Total cuent density, nom (A/m) Min: Min: x05 ANSYS.8 Total cuent density, nom (A/m) COMSOL Ac-length Figue 4 Vecto and contou field of Loenz foce nea the bottom electode; Cuent density distibution j on distance 0,5 R fom anode. Next the axisymmetic model of the electic funace was studied, whose fom and size coespond to the industial steel smelting funace (Fig. 3). This model was woked out to study electomagnetic fields in the liquid steel. The intensity and chaacte of the votex electomagnetic foces in all the volume and nea the bottom electode. Some esults of the calculations fo the industial funace model poblem by using the calculation methods woked out on the pevious model. Fig. 5 shows the fields of the cuent

7 Int. Jnl. of Multiphysics Volume 4 Numbe (ace: nom)_emqap*nomb_emqap (N/m 3 ) Aow: (Jz_emqap.*Bphi_emqap, J_emqap.*Bphi_emqap)(N/n 3 ) Max: 3.95e x Min: 5.50e Time = Slice: F (N/m 3 ) Aow: (F_x, F_y, F_z) (N/m 3 ) Steamline: Total cuent density (A/m 3 ) Max:.760e4 Max: x0 4 MN Y 0.04 Z X MX Min: 6.49e-7 Min:.364e-3 Figue 5 Field module of cuent density and Loenz foce vecto nea the bottom electode and oto Loenz foce; Field module and vecto Loenz foce, cuent steam line nea the bottom electode. 3D fomulation. density fo the model, the vectos of the Loenz foce in the aea of the bottom electode, as well as oto (votex) of the Loenz foce in the same aea. These esults allow to assess the foces intensity, causing the votex motion nea the anode. The simila analysis fo the model poblem was caied out in 3D vaiant. In Fig. 5 you can see the esults fo diffeent pefomances. You can see that the esults take fom axisymmetic D and spatial 3D pefomances ae the same. Howeve, the calculations fo

8 358 Modelling Votex Fields in Metal Smelting Funaces 3D ae seveal times moe time consuming. Theefoe, it is easonable to pefom the analysis axisymmetically. The calculations let us come to the following conclusions. The suggested models and methods allow to calculate electomagnetic and foce fields fo the electic funace model. It was stated that maximum value of the magnetic field induction, cuent density and the Loenz foce ae located ight nea the anode (bottom electode) at the distance of about the adius of the electode. The fathe fom the anode, the lowe ae the values. Accoding to the estimations, voluble density of the Loenz foce makes up about 30% of the gavity foce. 6. CONCLUSIONS The physical pocesses in the electic steel smelting funace have been studied. It is poved that the spatial distibution of the cuent in the funace leads to electo votex motion of the liquid metal. To descibe the pocesses in the electic funace the model of the magnetic hydodynamics is adopted. This model takes into account the spatial distibution of the cuent, electic and magnetic fields, tempeatue, the Loenz foce, the Joule heat and convection. The stategy of solving the stated conjugate poblem is woked out, the methods of calculating electomagnetic fields in ANSYS have been woked on, the effect of the conditions bounday of the calculated aea on the paametes of the cental zone is assessed. The esults of the calculations in ANSYS ae compaed with analytical assumptions, expeimental data and calculations in COMSOL. Similaity of the calculations done by diffeent methods poves the eliability of the methods and significance of the esults. REFERENCES [] J.A.T. Jones, B. Bowman, P.A. Lefank, R.J. Fuehan: Electic Funace Steelmaking in the Making, Shaping and Teating of Steel, The AISE Steel Foundation: Pittsbugh, Edito 998, P [] [3] [4] V. Bojaevics, Ya. Feibegs, E.I. Shilova and E.V. Shcebinin: Electically induced votical flows, Kluwe academic publishes, 989, P [5] L.D. Landau and E.M. Lifshitz: Couse of Theoetical Physics. Volume VIII. Electodynamics of Continuous Media, nd Edition, Buttewoth-Heinenann, 000, P [6] V.S. Ryaben kii, S.V. Tsynkov, V.I. Tuchaninov: Global discete atificial bounday conditions fo timedependent wave popagation, Jounal of Computational Physics, 00, No 74, P [7] D. Tif and T. Petila: Basics of fluid mechanics and intoduction to computational fluid dynamics, Spinge Science + Business Media Inc, Boston, 005, P [8] ANSYS: Theoy Refeence. Electomagnetic Field Fundamentals, Ninth Edition, SAS IP, Inc. [9] I.N. Budilov, Ju.V. Luckachuk: Modelling of magneto hydodynamics pocesses in industial electolysis cell in ANSYS, ANSYS solution. Russian edaction. Engineeing and technical jounal, autumn 007, P. 3-8 (in Russian)