DC FURNACE CONTAINMENT VESSEL DESIGN USING COMPUTATIONAL FLUID DYNAMICS

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1 DC FURNACE CONAINMEN VESSEL DESIGN USING COMPUAIONAL FLUID DYNAMICS B. Henning 1, M. Shapio and L.A. le Gange 3 1 B. Henning, DC Ac Funace Division, Bateman Metals, South Afica. bennie.henning@batemanbv.com M. Shapio, DC Ac Funace Division, Bateman Metals, South Afica. mike.shapio@batemanbv.com 3 L.A. le Gange, CFD Softwae Develope, Flo, South Afica. louis@softflo.com ABSRAC Effective pyometallugical pocess vessel design equies accuate assessment of the heat fluxes though the walls of the funace. his is paticulaly impotant fo feee lining opeation which is designed to potect efactoy mateials exposed to chemically coosive molten contents, o facilitate high tempeatue opeation when the efactoy mateials ae used at conditions close to thei sevice limits. Numeical modelling of fluid flow and heat tansfe in pocess vessels is often used to aid in the design of pocess vessels. Sophisticated models ae used to analyse the thee dimensional flow and heat tansfe pedicting the ects of electical heating, magnetic stiing, buoyancy, shea foces, vaious cooling ects and ultimately heat fluxes at the walls of the funace and efactoy. aditionally these models ae applied to the sepaate single fluid systems in a vessel such as the feeboad egion including the ac, the slag egion and the metal bath. Bounday conditions such as shea foces and heat fluxes between connecting egions such as the slag and metal bath ae eithe estimated o caied ove fom sepaate solutions. Shotcomings in these taditional appoaches include the estimation of sometimes citical bounday conditions leading to uneliable heat flux calculations. Also when bounday conditions ae caied ove between solutions, the pocess is difficult to set up, time-consuming and finally not fully coupled. In this pape the definition and esults of a fully integated numeical model of a complete ac funace ae pesented. he most impotant mechanisms acting in an ac funace wee consideed, including the fields of electical potential, cuent, magnetism, momentum, heat tansfe and adiation. empeatue dependant popeties included electical conductivity, density, viscosity, and themal conductivity. he geomety consists of the feeboad, the ac, slag, metal baths and diffeent efactoy egions. Although the combined model of ai, slag and metal would be defined as a multi-phase poblem it is not solved as such. Instead the diffeent fluids ae sepaated by sets of special solid baffles. hese baffles allow the implicit tansfe of cuent, magnetism, heat tansfe and shea foces between the diffeent fluids and disallow mixing of the sepaate fluids. he stengths of the integated model ae theefold: Fistly, it povides obustness in defining the geomety and bounday conditions fo the oveall model. Secondly, it povides the capability to switch on and off individual mechanisms such as buoyancy, magnetic stiing and shea foces in ode to obseve thei individual impotance. Finally, it povides a useful tool in the design pocess though its ability to obtain esults of paamete changes in shot time scales. 1. INRODUCION High intensity pyometallugical smelting and melting pocesses employing DC plasma acs as the enegy input souce have inceased the demands on the pefomance of the containment vessel efactoy lining. DC funaces nomally opeate with open baths in which molten pocess liquids ae in diect contact with the efactoy lining. he high eaction kinetics associated with vigoously stied baths educes black top fomation of un-eacted mateial floating on the slag suface, theeby inceasing feeboad-opeating tempeatues by adiation and convection. his combined with pocesses involving chemically aggessive Poceedings: enth Intenational Feoalloys Congess; 1 4 Febuay 004 INFACON X: ansfomation though echnology Cape own, South Afica ISBN: Poduced by: Document ansfomation echnologies

2 slag and supeheated phases have made undestanding the influence of the ac on velocities and tempeatue gadients within the molten bath citical to successful vessel design. he open ac offes significant additional opeating flexibility, as the total ective funace esistance can be adjusted by opeating with diffeent ac lengths, theeby ensuing maximum powe input ove a wide ange of bath esistance. his change in distibution of total powe between the ac and the bath esults in a tadeoff between excessive adiation loading in the feeboad and inceasing foced convection in the bath. Bath convection has a diect influence on feee lining thickness and mechanical stability, and it also affects the eosion of potective patially eacted aw mateial side wall banks. Highe bath convection film coicient inceases the efactoy hot face tempeatue. he goal of this eseach was to develop a paametic model in a suitable Computational Fluid Dynamics CFD package, which would enable both design and opeating paametes to be assessed and optimised. he development plan included: Applying fundamental bounday conditions of cuent, anode potential and extenal tempeatues to limit the numbe of assumptions equied fo model geneation. Inclusion of tempeatue dependant popeties if published. Analysis within a single model without the need to tansfe patial esults between sub-analysis steps. Conjugate heat tansfe 1 to obviate the need fo assumptions of convection heat tansfe coicients. oule esistance heating estimated diectly fom cuent distibution, and local esistivity. Paametic mesh geneation to enable the geomety and bounday condition to be conveniently vaied without the need to stat each model fom fundamental input commands. Contol of elaxation factos and othe numeical methods to ensue stability duing the solution, which would be applicable to a wide ange of geometies and opeating paametes. Post pocessing to allow convenient intepetation and compaison of esults. Funace design paametes include: Oveall funace geomety. Cooling systems. Refactoy composite selection based on themal conductivity. Funace opeating paametes include: Funace inventoy levels and tapping cycle management. Selection of funace electical opeating paametes volts and amps to achieve a cetain input powe, ac length popotional to opeating voltage.. APPROACH MEHODOLOGY he solution of the velocity, pessue and tempeatue fields in an atmospheic DC Plasma Ac has been well published in the liteatue [1,,3,5,6]. In addition to the solution of the tubulent tanspot equations, and consevation of mass, momentum, and enegy, the Maxwell equations have to be solved fo the Loent foces as an additional souce tem in the momentum consevation equations efe to Appendix A fo the bief desciption of the consevation and MHD equations [3], [5]. Simplified Maxwell equations may be solved because the flow satisfies the assumption associated with the magneto hydodynamic flow MHD appoximation [3], [5]. Papes have also been published on models and solution techniques which have been developed to include the inteaction of the ac with the molten bath, and combine vaious souce tems of the oveall flow to establish which dominates in a given pocess [4,6]. hese geneally involve sequential type analysis because the ac flow influences the foced convection of the fluid with which the moving feeboad gases ae in contact. Buoyancy diven convection, magnetic stiing and othe momentum souces in the bath does not significantly influence the ac. 1 Simultaneous, coupled heat tansfe within a fluid and an adjoining solid. Post-pocessing of numeical esults, whethe data o visual epesentation.

3 In ode to achieve the goals of this eseach, and genealise the ac and bath models to include fo multiple liquid ones, and conjugate heat tansfe in the efactoy mateial in contact with liquid ones, the development team of Flo was appoached to incopoate the Loent Foces as well as cathode and anode phenomena, following the appoach of onas Alexis [3], [5]. his substantially educed the oveall time to develop the ac-bath model, because the pe-pocesso, conjugate heat tansfe and post pocesso modules wee aleady completed and thooughly tested. In ode to handle multiple fluid egions, and additional govening equations at the anode and cathode, baffle cell goups wee developed. he baffle cell goup is a suface element with the following popeties: Sepaates and confines each egion to avoid analysis of the fee suface between the feeboad and the slag, which would othewise equie full tansient analysis instead of the quasi-steady state appoach adopted. Withstands a pessue diffeential acoss the baffle to pevent the sepaated fluids fom mixing. Facilitates continuity of conduction mechanisms, including heat flux, magnetic and electical fields. Ensues shea foce equilibium acoss the baffle by a numeical appoximation in which the momentum equation fo cells adjacent to the baffle is solved using a combined viscosity between the two fluids. Pescibes special bounday conditions including cathode cuent density distibution, cabon sublimation tempeatue, hompson Effect, Electode Condensation, Anode Potential [5]. Post pocessing to enable heat fluxes between egions to be extacted. he code makes povision fo switching flow and heat tansfe mechanisms in diffeent egions off and on, as well as vaying numeical damping factos at diffeent times duing solution. hese featues ae contolled by use defined sub-outines which enable the model to be solved sequentially, as well as allowing the coupled fields in each one to build up gadually and quasi-simultaneously. his pseudo-tansient appoach pomotes numeical stability duing the initial pat of the solution. All ones ae solved simultaneously and implicitly in pseudo-steady state when the fields in each one ae sufficiently established. he code and use defined sub-outines wee tested fo numeical stability and consevation of tanspot mechanisms. 3. NUMERICAL MODEL Pototype model geomety was developed based on a typical DC Slag Cleaning Funace ated at 40 MW. Howeve the input powe was limited to 5 MW, which coesponds to the heat loss fo a funace of this sie. A pocess enegy dissipation sink has not yet been incopoated. he model configuation and position of the baffle cell goups is shown in Fig. 1. he model epesents a 5-degee slice of the funace with cyclical bounday conditions on the vetical slicing sufaces to peseve the symmety. Othe key model paametes wee: Input cuent 0 ka held constant whilst ac length was vaied. Opeating Powe 5 MW to appoximate heat loss conditions no pocess enegy supplied. Electode Extenal Diamete 600 mm. Heath Intenal Diamete 9m. he model is divided into 4 main egions as shown in figue 1: he ac and uppe feeboad egion. he maximum cell sie in the ac egion coesponds to the cathode spot adius, detemined by the applied cuent 3. A adiation model based on a tempeatue-enegy density look-up table is included as a heat tansfe mechanism in this aea to tansfe heat fom the ac to the slag suface and the efactoy walls with tempeatue-dependant physical popeties [3], [5]. Slag bath with constant physical popeties typical of Silica-Ion Oxide Slag [6]. Depth of slag at the top of the metal bath = 0.55m, which is the typical inventoy fo a 40 MW funace. Metal bath with constant physical popeties typical of molten steel [6]. Depth of metal at the lowest point of the heath = 0.5m, which is the typical inventoy fo a 40 MW funace. Refactoy lining with constant physical popeties typical of a DC Funace set-up. 3 R C = I/π C

4 Figue 1. Composite layes of the numeical mesh fo a typical DC Ac Funace. he model equies 5 main baffles to link the fluid and efactoy egions: ip of the electode cathode and ac egion inteface. his aea incopoates the necessay modelling of the cathode spot. Slag-feeboad inteface. Selected aeas include povision fo modelling of anode phenomena. his aea incopoates a pedetemined, non-equilibium ac depession one to investigate the deflection of the hot gas in the ac away fom the slag suface, and towads the uppe side walls above the slag-feeboad inteface. Slag- metal inteface. Metal-heath inteface. his baffle incopoates the anode potential bounday condition. Molten slag, metal, ac and feeboad efactoy intefaces. empeatue and heat flux bounday conditions include: 4300 K fixed electode tip tempeatue cabon gaphite sublimation tempeatue K fixed electode vetical suface tempeatue K fixed inside funace oof tempeatue to simulate foced cooling of the oof. Adiabatic top of side wall suface. 303 K fixed cold face efactoy tempeatue.

5 he following assumptions wee made in the development of the numeical model: he ac geomety is axi-symmetic and time independent. he cuent distibution in the ac column is paabolic [5]. Heat conduction and intenal heat geneation in the electode was ignoed he velocity, tempeatue, magnetic and othe fields wee allowed to develop ove a numbe of time steps as if the vaious physical phenomena wee gadually switched on ove time. When the fields ae changing slowly, quasi-static, the model is conveted to a time independent analysis. Logaithmic wall functions wee incopoated in the wall bounday specification [7] instead of solving the detail bounday layes necessitating vey fine gids. 4. DISCUSSION OF HE NUMERICAL RESULS Fo illustation puposes, the tempeatue and velocity fields in the ac and feeboad egions ae shown at an ac length of 16 cm in Figues to 5. he velocity and tempeatue fields in the slag bath ae shown in Figues 6 and 7 and the velocity and tempeatue fields in the metal bath ae shown in Figues 8 and 9. All tempeatues ae in Kelvin and elative to eo Kelvin. Figue. empeatue contou distibution in the ac egion. Figue 3. empeatue contou distibution in the feeboad. Figue 4. Velocity vecto distibution in the ac egion. Figue 5. Velocity vecto distibution in the feeboad.

6 Figue 6. Velocity vecto distibution in the slag bath. Figue 7. empeatue contou distibution in the slag bath. Figue 8. Velocity vecto distibution in the metal bath. Figue 9. empeatue contou distibution in the metal bath. he ac induces a clockwise ciculation patten as viewed in the slag as a esult of the foced convection at the slag-feeboad inteface. he slag induces a counte clockwise ciculation patten in the metal as a esult of shea coupling acoss the slag-metal baffle. he buoyancy-diven flow and shea induced flow ae mutually einfocing in the slag. In the metal, the shea- and buoyancy foces oppose, but the shea foces dominate. he model was epeated with ac lengths of 16, 0, 30, 34 and 38 cm. Figue 10 demonstates that as the ac length inceases, the ac is cooled by additional entained feeboad gas. he ect of ac length on the ac gas velocity is shown in Figue 11. his demonstates that the ac velocity inceases because the ions in the plasma ae acceleated acoss an inceasing potential as the ac length is inceased.

7 empeatue K cm 0cm 30cm 34cm 38cm Velocity m/s cm 0cm 30cm 34cm 38cm Distance fom cathode upto 18cm Distance fom cathode upto 18cm Figue 10. Axial ac tempeatue vs. axial distance fom the cathode at a cuent of 0kA. Figue 11. Axial ac velocity vs. axial distance fom the cathode at a cuent of 0 ka..75e E05 6 Cathode fall heat W.65E05.60E05.55E05.50E05.45E05.40E05.35E Ac length cm Heat Flux kw/m² 4 Ai 0 18 Metal Slag Ac length cm Figue 1. oule heating vs. diffeent ac lengths at a cuent of 0kA. Figue 13. Side wall heat fluxes vs. diffeent ac lengths at a cuent of 0 ka. he cathode fall heat 4 in Figue 1 futhe illustates that the ac voltage inceases as the ac length is inceased. Cathode fall enegy is as a esult of oule heating in the ac. At constant cuent, the ac potential inceases popotionally with ac length, esulting in an appoximately popotional incease in esistive powe dissipation. he dependence of the lowe side wall and uppe side wall heat flux on the ac length is shown in Figue 13. he heat flux convected to the lowe side walls educes slightly with longe ac length, but the additional powe in the ac inceases the uppe side wall heat flux in a simila atio to the cathode fall heat flow ate. his indicates that lowe side wall feee lining opeation can be optimised by adjusting ac length, povided that obust efactoy mateials ae selected fo the uppe side walls. 5. CONCLUSIONS he definition and esults of a numeical model of an integated ac funace wee pesented. he model was implemented in the Flo CFD code and povides fo the implicit solution of electical and magnetic fields, fluid flow and heat tansfe though the entie funace. he esults indicate that the model is intenally consistent with expeimental obsevation of the esponse to changes in ac length. he model is capable of assisting with the design of the pyometallugical containment vessel geomety, cooling systems and efactoy composite, as well as poviding valuable infomation on optimisation of funace electical opeating paametes. 4 Q C = C V C [5]

8 6. FUURE DEVELOPMENS he eseach completed to date indicated that in ode to make the modelling esults moe compaable to commecial opeation, and incease the ectiveness of the design tool, the following featues have to be developed: Model validation with expeimental data. Model sensitivity to mesh efining to optimise pocessing un time. Impoved adiation model including povision fo adiation absobtivity of gas cloud especially in the ac this is cuently in pogess. Full smelting/ melting model to account fo pocess enegy and enable diffeent feed positions to be investigated. Modelling the ect of chemical eactions in the melt especially CO evolution in the bath as a convective souce tem. Ac depession one and fee suface tansient analysis between the feeboad and the slag. Dynamic, time dependant ac. 7. REFERENCES [1] Ushio, M., Sekely,., and Chang, C.W., Mathematical modelling of flow field and heat tansfe in high-cuent ac dischage, Ionmaking and Steelmaking, 1981, no. 6, pp [] Sekely,., McKelliget,. and Choudhay, M., Heat-tansfe fluid flow and bath ciculation in electicac funaces and dc plasma funaces, Ionmaking and Steelmaking, 1983, vol. 10, no.4, pp [3] Alexis,., Ramie, M., apaga, G., and önsson, P., Modeling of heat tansfe fom an electic ac a simulation of heating Pat I, Electic Funace Confeence Poceedings, 1999, pp [4] Ramie, M., apaga, G., Alexis,., and önsson, P., Effects of the Ac, Slag and Bottom bubbling of agon on the fluid flow and heat tansfe of a DC EAF Bath Pat II, Electic Funace Confeence Poceedings, 1999, pp [5] Alexis,., Ramie, M., apaga, G., and önsson, P., Modeling of a DC Electic Ac Funace Heat ansfe fom the Ac, ISI Intenational 000, vol. 40, no. 11, pp [6] Ramie, M., apaga, and McKelliget,., Fluid flow and heat tansfe in steel o steel/slag baths of a DC electic ac funace unde the influence of the ac and gas injection, Pape pesented at the Bimacombe Memoial Symposium, 4 Octobe 000, Vancouve, Bitish Columbia, Canada. [7] Launde, B. E., and Spalding, D.B., he numeical computation of tubulent flow, Comp. Meth. in Appl. Mech. & Eng., vol. 3, 1974, pp. 69.

9 APPENDIX A anspot Equations he govening tanspot and tubulence equations fo the ac ae expessed in two-dimensional cylindical coodinates as follow: Consevation of mass: 0 1 = w v 1 whee: = density, = adial distance and = axial distance. he tems v and w ae the velocity components in the adial diection and axial diection, espectively. Consevation of the axial momentum and the axial Loent foce: B w v v P vw v θ = 1 1 whee: = ective dynamic viscosity, P = static pessue, = cuent density in the adial diection and B θ = magnetic flux density in the aimuthal diection. he poduct B θ is the axial component of the Loent foce poduced by the cuent and the induced magnetic flux density in the solution domain. Consevation of the adial momentum and the adial Loent foce: B v w v w P w vw θ = 1 3 whee: = cuent density in the axial diection. he poduct B θ is the adial component of the Loent foce. Consevation of themal enegy and the adiation sink tem: = C C e k S v v p p b R e σ σ σ 4 whee: = tempeatue, C p = specific heat at constant pessue, σ = themal conductivity, σ e = electical conductivity, S R = adiation sink tem, k b = Bolmann constant and e = electon chage. ubulent tanspot equations he well-known high Reynolds numbe k-ε model has been used and will not be discussed in this pape due to space limitations [3], [5], [7]. MHD Appoximation As seen above, the equations fo consevation of the axial and adial momentum 3, include souce tems fo the Loent foces. hus Maxwell s equations need to be solved. In flows in which the electic field is of the ode of magnitude of the induced quantity V B, cetain simplifications can be made fo Maxwell s equations. his type of flow is usually efeed to as MHD magnetohydodynamic flow.

10 he following assumptions wee made fo the MHD appoximation [5]. /V/²<<c², whee c is the speed of light. he electic field, E, is in the ode of V B. he electic enegy is negligible compaed to the magnetic enegy. In Ohm s law space enegy may be neglected. he foce density is epesented by: f = e E B 5 Also, fom the Maxwell stess tenso, the electic tems can be shown to be negligible compaed to the magnetic tems in this case. Fo this eason e E is taken as negligible in the foce density equation [5]. In a two dimensional axis-symmetic system the adial and axial components of the souce tems in the momentum equation can be witten as: F F = B 6 θ = B 7 hus, in ode to detemine these souce tems the cuent density and the aimuthal magnetic flux density have to be calculated using an MHD appoximation. he necessay Maxwell s equation may be witten as: whee: is the cuent density. Also, fo a moving fluid, Ohm s law takes the following fom: θ = 0 8 [ E V B] = σ e 9 whee the fist tem inside the paenthesis that is, the electic field, E defines the applied cuent app and the second tem defines the induced cuent i. he electic potential is given by: E = Φ 10 Duing the development of this model it was assumed that the induced cuent tem could be neglected, that is the magnetic Reynolds numbe << 1. heeafte, equations 8, 9 and 10 wee combined to obtain the following elationship: σ e Φ = 0 11 Equation 11 is solved numeically to obtain the electic potential, which is then used to calculate the total cuent using Ohm s law, equation 9. heeafte, Ampee s law is employed to appoximate the aimuthal magnetic flux density. Fo an axis-symmetic model this is done as follows: p Bθ = d 1 whee: p = magnetic pemeability in the media. In these calculations p is assumed to be equal to o. Fo futhe detail egading the simulation of heat tansfe fom an electic ac, including the cathode and anode bounday layes, efe to one of the jounal papes of onas Alexis [3], [5]. 0