Numerical simulation of interaction during the top blow in a steel-making converter

Numerical simulation of interaction during the top blow in a steel-making converterHranislav Milosevic a ,Svetlana Stevovic b ,⇑,Dojcin Petkovic aa Serbian University Pristina,PMF Kosovska Mitrovica,SerbiabFaculty of Construction Management,University Union,Belgrade,Serbiaa r t i c l e i n f o Article history:Received 28February 2011Accepted 16May 2011Available online 14June 2011Keywords:Numerical modeling Interaction Turbulent flow Navier-Stokes Flow structurea b s t r a c tThe numerical modeling of interaction between oxygen high-pressure jets and a liquid–metal surface in a steel-making converter,where,under the force action of the jets,a cavern with a hydrodynamically unstable surface forms in the metal bulk,is studied.A simplified scheme of chemical reactions and mech-anisms of metal-drop dispersing from the interface between the phases is proposed.This scheme permits an adequate description of the hydrodynamic flow pattern in the cavern.The modeling of a two-phase turbulent flow in the cavern is considered within the framework of the continuum model based on the averaged Navier–Stokes equations.To close the equations,a modified k –e turbulence model is used,which takes into account the presence of the second phase.The flow structure in the cavern is studied.Practical recommendations for increasing the efficiency of the carbon-monoxide afterburning process in the cavern are given.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionThe top blow of a cast-iron bath in a steel-making converter is used to burnout the dissolved carbon,which is the essence of the cast-iron-to-steel conversion [1].The blow is conducted using a system of high-pressure supersonic and subsonic oxygen jets impinging on the cast-iron bath surface.Under the force action of these jets,a gas cavity (cavern)with a hydrodynamically unsta-ble interface between phases forms in the metal bulk [26].From this surface,an intense dispersing of finely dispersed metal drops into the cavern proceeds,which causes a manifold increase in the surface area where the interaction between the metal and oxy-gen takes place.The main gaseous products of this interaction are CO and CO 2[29],and,to increase the efficiency of the conversion process and to decrease the amount of harmful effluents,one should raise the afterburning degree of CO and CO 2in the working volume of the converter by improving the scheme of the top blow-ing [28].The studies in this direction are an urgent matter for all con-verter plants of Russia [18]and all other CIS countries [20]since the waste gases are not recovered there for their subsequent use as a fuel.On the whole,the problem of carbon monoxide afterburn-ing inside a converter is the object of numerous studies [23,25].However,up to the present time,it has found no satisfactory solution [16]because of the complexity and poor understandingof processes that proceed during the interaction of oxygen with cast iron [17].In this work,an attempt is undertaken to consider the gasdynamic aspect of the problem,with due regard for both the formation of a cavern and the structure of a two-phase flow in it,and with allowance for the occurrence of nonequilibrium chemical reactions.2.Physical model of the processA typical scheme of the top blow is shown in Fig.1.Through a special vertical tube (lance),commercially pure oxygen is fed,which flows out of a multi-nozzle head in the form of a system of sub-and supersonic jets of an adjustable strength of their action on the metal surface in the bath [2].In this way,conditions are pro-vided for a controlled steel melting with minimum losses of metal and for increasing the effectiveness of the off-gas afterburning in the converter without any substantial deterioration of its firebrick lining.According to data reported in (1),the refinement of the metal under the action of oxygen proceeds in two stages,the first one being metal oxidation with the predominant formation of ferric oxides (initial reaction zone)and the other being interaction of these oxides with chemical elements dissolved in the metal bath (secondary zone).The main gaseous reaction product in the sec-ondary zone is carbon monoxide which is released from the reac-tion bed and incomes into the gas cavity where its partial afterburning takes place as it interacts with the oxygen jets accord-ing to Milosevic [12].Although the conversion of the cast iron into the steel is described by a system of several tens of chemical reactions (1)an insight into the gasdynamic flow pattern in the0017-9310/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.ijheatmasstransfer.2011.05.018⇑Corresponding author.E-mail addresses:mhrane@ (osevic),svetlanas123@ (S.Stevovic),dojcin.petkovic@ (D.Petkovic).cavern can be gained,as studies showed,by considering the fol-lowing simplified scheme of the process:–the liquid phase includes the melt with 4%of carbon (C)and 96%of metal (Fe);–at the interface between the phases,the only generalized reac-tion of carbon combustion takes place:2C þO 2¼2CO;ð1Þ–the afterburning of the carbon monoxide proceeds in the cavern through a gas-phase reactionCO þO 2¼CO 2;ð2Þ–at the gasdynamically unstable gas/metal interface,liquid–metal drops (shots)form,which enter the cavity.At the surface of the drops,reaction (1)proceeds as well;–formation of slag-metal emulsion on the metal surface is ignored.3.Mathematical modelSince,as already noted,the main objective of this work is a study of the gasdynamic aspect of the process of interest,we simplify the real scheme of the top blow shown in Fig.1and assume that the flow is axisymmetric and the lance ends in a hemisphere,from the surface of which two jet of commercially pure oxygen flow are ejected (Fig.2):a central (supersonic)jet and a side (subsonic)jet whose inclination can be varied.In this axisymmetric formulation,theside jet is a fan one,which well models the multi-nozzle design of real heads (2).Next,we assume that the jet efflux is steady,the shape of the interface is not known beforehand and is given by the condition of equality between the gas-phase pressure and the hydrodynamic pressure in the liquid metal at each point of the interface.The flow in the gas cavity of the cavern contains sub-and supersonic zones and shock waves,and is two-phase and turbulent.Additionally,the following assumptions are adopted:–the motion of the gas phase is ignored,and only the hydrostatic pressure is taken into account;–the gas phase includes five components,O 2,CO,CO 2,N 2and H 2O,with the only chemical reaction (2)proceeding in it;–the mass concentration of carbon in the metal is assumed con-stant since the characteristic duration of the gasdynamic pro-cesses proceeding in the cavern is by several orders of magnitude shorter than the converter melting duration.The components N 2and H 2O are assumed neutral.The presence of molecular nitrogen is caused by its presence in the air which can be sucked by the supersonic jet into the cavern from the ambient space.The presence of steam,as was noted in [3],is necessary for the occurrence of reaction (2),the complete scheme of its for-mation being,however,rather complex and concentration small (within 0.1%[1]).Therefore,in the present study it is assumed that H 2O incomes from the interface in the above-indicated concentration.To describe the flow of interest,a continual approach was used,within which the system of governing equation written in the vec-tor-tensor form isr ðy q ~UÞ¼yJ ;ð3Þr ðy q ~U ~U Þþr y q Àr ðy s Þ¼y q p C R ð~U p À~U ÞÀJ ~U p h i ;ð4Þr y q ~Uh Àk r T hi¼~U r yp þy U þq p C k ðT p ÀT ÞþC R ~U p ð~U p À~U Þn o h i;ð5Þr y q ~Uk Àðl trþl Þr k hi ¼Àyl t @u t @x k þ@u k @x t&þ23q k þl t @u i @x l d ik !@u t@x k þq e þe s þe JÀÁ'ð6Þr y q ½C i ~U ÀD i r C i ¼yJ i ði ¼1;...;5Þ;ð7Þk ¼c plPrþl tPr t;D ¼lScþl tSc t;p ¼q TR 0X 5i ¼1C i =M i ;ð8Þr y ðq p ~U p þh q 0p ~U 0p iÞ¼yJ p ;ð9Þr y ðq p ~U p ~U p þ~U p h q 0m ~U p iÞþr y q p h ~U 0p ~U 0p i ¼y q p C R ð~U À~U p Þ;ð10Þr y ðq p ~U p þh q 0m ~U p iÞh p þr y q p h h 0p ~U 0p i¼y ½q p C a ðT ÀT p ÞþJ p q ;ð11ÞJ ¼J 2ÀJ 1;J p ¼ÀJ ;J 3¼J 4¼J S ¼0;osevic et al./International Journal of Heat and Mass Transfer 54(2011)4275–4279where s and U are the viscous-stress tensor and the term allowing for dissipation owing to viscous forces in the averaged Navier–Stokes model(s also includes,through the dynamic viscosity l ef=l+l t the turbulent-stress tensor);l t is the turbulent dynamicviscosity;C R is the aerodynamic drag coefficient of a particle,C a the heat-transfer coefficient from a particle to the gas[15];the sub-scripts1–5and p refer to the gas components O2,CO,CO2,N2, H2O and the particles,respectively;J1is the massflow rate of O2, J2is the formation rate of CO2;M i are the molecular masses of the components;and k and e are the kinetic turbulent energy and its dissipation rate.The values of the coefficients C R and C a and those of correlations between thefluctuating parameters of the particles were deter-mined from the average parameters of the gas-carrier using the expressions reported in[4]and the terms e s and e J allowing for the additional dissipation k on the particles were borrowed from [5].In the stagnation region of the impinging jet,a modification of the k–e model proposed in[6]was used with correction of the turbulence model constant adopted for the free-flow region of the jet[7].In the calculation of the carbon-monoxide combustion rate,the gas-phase turbulence was taken into account so that the combus-tion rate was found from the expressionJCOÀmin f J ch;J tb g;J ch ¼1:3Á1014expðÀ30;000=RTÞC COffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC O2C H2Oq;J tb ¼A qekmin C O2;C COs&';where J ch is the rate of the generalized chemical reaction of CO com-bustion taken from[8]and allowing for the effect of steam concen-tration on the combustion;J tb is the turbulent mixing rate given by the turbulent-vortex fragmentation model[9];s is the stoichiome-tric coefficient,and A is an empirical constant(A=2).The solution of system(3)–(11)was sought in the domain shown in Fig.2,which was covered by a rectangular irregular dif-ference grid.At the domain boundaries,taking into account the flow symmetry,the following boundary conditions were set:-at the exit sections of the nozzles(HK and FG)installed on the lance,the mass-flow rate of oxygen,the sloping angle of the jets to the symmetry axis,and the stagnation temperature equal to the ambient value were set;-at the interface AED between the phases,a constant pressure equal to the hydrostatic pressure in thefluid and the adhesion condition for the gas phase were set.The mass inflow rate of CO from the surface was determined from the carbon combustion reactionJCO¼ðM CO=M CÞq C O2q C K C expðÀE=RTÞ;where q C is the carbon mass concentration in the metal,K C–2Á105m/s and E=À158,000J/mole,and for CO the following boundary condition was set:q C COÀq D CO q C CO¼J CO;where D CO is the diffusion coefficient and n is a normal to the sur-face.For the other components of the mixture,the nonpenetration condition at the surface was used;–at the symmetry axis AA,the conditions offlow symmetry were set;–at the outlet boundary CD and at the boundary BC,‘‘soft’’bound-ary conditions and conditions imposed by the environment(air at the standard conditions),respectively,were used.An approach is proposed to describe the dispersion of the metal drops from the interface.This approach is based on the following representation of the process:the interface is assumed to be‘‘stable in the mean’’,and,from it,finely dispersed liquid–metal particles income into the gas cavity.The sizes of the particles and the inten-sity of their income are determined by the velocity characteristics of the gas stream moving along the tangent line to the interface[14], as well as by the physical properties of the two phases[21].To determine these parameters,we consider the interaction process between the phases as a result of theflow around a curvilinear impermeable surface covered by a liquid,evaporating metalfilm by the gasflow.Thefilm can be defragmented into drops owing to Taylor instability,and its behavior,as the experiments[10,11] show,turns out to be unstable in the case when the rate of the transverse mass blowing from thefilm surface becomes comparable with the mass-flow rate of the gas phase,the gas-phase velocity being directed along the a parameter that characterizes the onset offilm defragmentation,the results of[11]were used:tangent line to the‘‘averaged’’interface.As a parameter that characterizes the onset offilm defragmen-tation,the results of[11]were used:q00q1=2U00lr Ar1=3ÃRe1=6>1:75;ð12ÞwhereArür3v2q3j~g;~s jð1Àq00=qÞ1=2;Re¼u00dv:Here U00is the modulus of the velocity vector of the gas which flows over the surface outside the boundary layer,q00is the gas density,q is thefluid density,r is the surface-tension coefficient of the liquidfilm,v is the kinematics viscosity of thefluid,ð~g;~sÞis the projection of the free-fall acceleration vector on the tangent to the surface,and d is thefilm thickness.From the experimental dependences,we found the following relation between the drop size and the gas-stream dynamic pressure:U002q00D0r P10;ð13Þwhere D0is the diameter of a drop at the moment the drop leaves the surface.Therefore,from expressions12and13,it is possible to determine the position of the onset of thefluidfilm fragmenta-tion and the sizes of drops originating from this process.To determine the mass income rate of the metal particles,prac-tical recommendations of[1]were used,according to which the mass income rate of the drops G p is3–5times higher than the mass-flow rate of oxygen passing through the lance.By virtue of the above,the following parametric dependence was used in the calculations:G p¼a G O2;ð14Þwhere the parameter a was assumed to run through a set of its val-ues,and the magnitudes of all parameters of the particles at the moving boundary AE were determined from the above relations. At the boundaries KF and BC,the conditions of the absence of parti-cles were used,and at the boundary CD‘‘soft’’boundary conditions were set[24,27].The numerical solution of the problem under study was found using the ELA–FINT method–a combined Eulerian–Lagrangian method for calculating incompressibleflows with moving bound-aries[13],which was modified to cover the case of incompressible flows[22].The smoothing procedure based on b-splines was also used,in order to determine‘‘the average in the mean’’interface.osevic et al./International Journal of Heat and Mass Transfer54(2011)4275–427942774.Some calculation results and discussionThe numerical modeling of the top blow was carried out to reproduce its initial stage,for which the carbon concentration in the metal is maximum.The Mach numbers of the central and the side jet,M 0and M 1were assumed to equal 1.2and 0.5,respec-tively.The sloping angle of the side jet to the lance was 45°.Three values of the parameter a in (14)were tried:a =2,4and 6.Fig.3shows the structure of the flow pattern in the form of the velocity vectors and Mach number contours in the cavern forming as a result of the interaction between the oxygen jet and the liquid-metal surface for (solid curve).For the two other values of this parameter,it is only the shape of the cavern that substantially changes (see the dashed curves in Fig.3b which correspond to a =4and 6),while the flow structure in the cavern does not change noticeably.As follows from Fig.3,the deceleration of the super-sonic jet occurs near the metal surface without its penetration into the cavern.Owing to the high difference between the jet and metal temperatures,the temperature and density of the gas phase in the cavern is essentially nonuniform,which results in the occurrence near the interface of the region with high gas velocities,which near the exit section of the cavern can exceed the sound velocity [19,24].Fig.4a s hows the profiles of particle concentration in various cross-sections of the cavern.The interaction of particles with the gas-carrier is seen to increase the particle concentration near the interface.This inhomogeneity results in that the main fraction of CO is released near the cavern surface,the main consumption of oxygen incoming into this zone due to both convective and diffu-sional transfer in reaction (2)taking place right here.However,this transfer,as follows from Fig.4b does not guarantee a sufficiently complete CO 2combustion,and its considerable fraction is carried away out of the cavern.Practically zero CO concentration near the jet axis is related to that here,owing to the low temperature and the lack of steam not reaching the oxygen-jet axis,reaction (2)does not proceed.An increase in the steam concentration by one order of magnitude leads to a profound growth of the com-pleteness of the CO combustion (dashed curves in Fig.4b).There-fore,taking measures aimed at intensifying oxygen transfer to the interface and increasing the steam concentration in the caverncan be considered as practical recommendations for increasing the effectiveness of the CO after burning process.5.ConclusionFrom the results obtained,the following conclusions can be drawn:1.A numerical algorithm for modeling the top burn of a steel-making converter is devised.This algorithm takes into account the CO after burning process in its accurate formulation.2.The structure of the two-phase flow in the cavern with allow-ance for the occurrence of chemical reactions in it is studied.3.Based on the analysis of the flow structure and some peculiar-ities of the CO after burning process,several practical recom-mendations are given for enhancing the effectiveness of the process.AcknowledgmentThis work was supported by the Ministry of Science and Tech-nological Development of Serbia,Grant No.TR35030.References[1]V.I.Baptizmanskii,V.B.Okhotskii,Physicochemical Foundations of the Oxygen-Converter Process,Vyshcha 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