Numerical Simulation of Desulfurization Behavior in Ladle with Bottom Powder Injection

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1 IIJ Internatonal, Vol. 58 (2018), IIJ Internatonal, No. 11 Vol. 58 (2018), No. 11, Numercal mulaton of Desulfurzaton Behavor n Ladle wth Bottom Powder Injecton Wentao LOU,* Xaoyu WANG, Zhuang LIU, en LUO and Maoyong ZHU chool of Materals and Metallurgy, Northeastern Unversty, henyang, Peole s Reublc of Chna. (Receved on June 6, 2018; acceted on July 13, 2018; J-TAGE Advance ublshed date: etember 12, 2018) A comutaton flud dynamcs oulaton balance model smultaneous reacton model (CFD PBM RM) couled model was used to redct the reacton knetc and desulfurzaton behavor n 80 ton ladle wth bottom owder njecton. The reacton rate and evoluton of mult-comonents ncludng Al,,, Mn and Fe at the owder drolet lqud steel nterface, bubble lqud steel nterface, to slag lqud steel nterface and ar lqud steel nterface were revealed. Then, the effects of dfferent knetc condtons on the desulfurzaton effcency were nvestgated, and the mortance of varous mechansms was dscussed and clarfed. The results show that at the lower owder njecton rate, the desulfurzaton s manly attrbuted to the jont effort of both owder lqud steel reacton and to slag lqud steel reacton whch s the revalng mechansm. At the hgher owder njecton rate, the owder artcle lqud steel and bubble lqud steel nterface reacton become more mortant and then redomnate the desulfurzaton behavor. Wth the ncrease of gas flow rate, the total desulfurzaton rato gradually decreases, and wth the ncreasng of owder njecton rate, the total desulfurzaton rato ncreases. KEY WORD: bottom owder njecton; desulfurzaton; reacton knetc; numercal smulaton; ladle. 1. Introducton Wth the ncrease of demands for hgh qualty and ultralow sulfur grade steel, hgh effcency of ladle desulfurzaton has become one of man objectves n the steelmakng rocess because sulfur n most of steel roducts s detrmental. Ladle bottom owder njecton (L BPI), s a new refnng technology that the fne refnng owders are njected nto lqud steel for desulfurzaton through bottom slot lugs n ladle, 1 5) as shown n Fg. 1. Ths technology has great otental to sgnfcantly enhance the refnng effcency and effectveness and to lower the cost due to tself better knetc condtons and technology features, and t may also overcome some roblems exstng n the tradtonal refnng rocessng, such as serous slashng, nflexblty, threat of cleanlness caused by to lance. In order to mlement ndustral alcaton of ths new technology, t s a key ssue to use L BPI to acheve hgher desulfurzaton effcency of lqud steel. Therefore, t s foundatonal and necessary to reveal clearly the slag-metalowder artcle multhase reactons and desulfurzaton effcency n ladle wth bottom owder njecton. Currently, the slag-metal two-hase reacton behavor n gas-strred ladle has been studed by many researchers. 6 15) However, the slag-steel-owder multhase reacton n ladle wth bottom owder njecton s stll rarely studed. As shown n Fg. 2, n the rocess of bottom owder njecton, the multhase Fg. 1. chematc dagram of new technology of ladle bottom owder njecton. (Onlne verson n color.) * Corresondng author: E-mal: louwt@smm.neu.edu.cn DOI: htts://do.org/ /sjnternatonal.iijint Fg. 2. chematc dagram of multhase flow transort behavor and reacton knetcs n ladle wth bottom owder njecton. (Onlne verson n color.) 2018 IIJ 2042

2 IIJ Internatonal, Vol. 58 (2018), No. 11 flow transort and chemcal reactons n ladle nvolve many comlex henomena, whch would occur smultaneously and nteract wth each other, and n turn would drectly determne desulfurzaton effcency and effectveness. In our latest lterature, 16) a mathematcal model had been develoed to descrbe the multhase flow and reacton knetc n the bottom owder njecton rocess, and model valdaton was carred out usng hot tests n 2 ton nducton furnace wth bottom owder njecton. In resent work, the objectves of resent work were to use the CFD PBM RM couled model to redct desulfurzaton effcency n 80 ton ladle wth bottom owder njecton. The mechansms of mult comonent smultaneous reactons ncludng Al,,, Mn, Fe and O at mult nterface ncludng to slag lqud steel nterface, ar lqud steel nterface, owder drolet lqud steel nterface and bubble lqud steel nterface were resented, and the effect of sulfur solublty n owder drolet on the desulfurzaton was also taken nto account. The reacton rate and evoluton of multle nterhase reactons nvolvng dealumnaton, deslcaton, demanganzaton and desulfurzaton were revealed. The effects of dfferent knetc condtons on the desulfurzaton effcency were nvestgated, and the mortance of varous reacton mechansms was dscussed and clarfed. 2. Model Descrton and Numercal cheme 2.1. Model tructure The model assumtons have been lsted n our revous work, 16) and the basc deas of the resent model are schematcally structured n Fg. 3. The entre model conssts of three man blocks,.e., a CFD block, oulaton balance model (PBM) block and smultaneous reacton model (RM) block. In CFD model, the local flow feld, volume fracton and turbulent energy dssaton rate were obtaned by solvng the mass, momentum and k ε turbulent equatons, as well, the seces mass transort model was solved to obtan the local content dstrbuton and overall removal rato of each seces n 80-ton ladle. Then the related arameters were transferred nto PBM and RM. In PBM model, by solvng the artcle artcle collson rate, artcle bubble adheson rate and artcle removal rate, the artcle sze and mass concentraton dstrbuton could be obtaned and then were transferred nto CFD and RM to udate the source terms of each equaton for the next tme ste. In RM model, the chemcal reacton rates at the to slag lqud steel slag ar nterface, ar lqud steel nterface, owder drolet lqud steel nterface and bubble lqud steel b nterface were calculated and transferred nto CFD to udate the source terms of seces transort equaton for next tme ste. In resent model, the convergence needs to be guaranteed n each tme ste n order to get more accurate redcted results, and the tme ste of 0.25 was selected. The teraton resdual was set to fall below at each tme ste for all the subsequent smulatons 2.2. CFD Model In the resent study, based on Euler-Euler aroach, the mass and momentum balance equatons are solved for each hase searately. The mass balance equaton of each hase whch can be exressed as k kuk k kuk k... (1) t where ρ k, α k, u k and k are the densty, volume fracton, averaged velocty vector and mass source term of lqud hase (k = l), gas hase (k = g) and owder artcle hase (k = ) resectvely. Both l and g are zero, and s calculated by PBM of artcles and dscussed later. For the momentum equatons, the drag and turbulent dserson force among three hases are consdered as momentum exchange source terms, and the detaled exresson for the gas-lqud-artcle three hase hydrodynamc equatons together wth the k ε turbulence model had been descrbed n our recent ublcaton 17) and would not be reroduced here Poulaton Balance Model (PBM) In the bottom owder njecton rocess, the owders artcle growth and removal behavor have a sgnfcant mact on the multhase flow transort and desulfurzaton knetc, and they would be descrbed by Poulaton Balance Fg. 3. Overall soluton schematc of the CFD PBM RM couled model. (Onlne verson n color.) IIJ

3 IIJ Internatonal, Vol. 58 (2018), No. 11 Model (PBM): u t N N V 1 1 N kj kj Vk, Vjnkn jkj j j j V, V nn k j1 2 1 j V tot, j 01,,,N 1... (2) kj V V 1 V V1 V1 Vag V1 V 0 otherwse forv V V 1 ag forv V V ag 1... (3) where ρ and u are the densty and velocty of the artcle hase resectvely, δ kj s assgned to 0 (k j) or 1 (k = j), V ag s the volume resultng from the aggregaton of two artcle, and α s the volume fracton of artcle sze, β(v, V j ) reresents the total coalescence rate between artcles due tot to a varety of collson mechansm, reresents the total removal rate from lqud steel due to a varety of removal mechansm. These arameters can be wrtten as j j TR j T j... (4) tot Wall IF BIB BIR BIR Wake... (5) where β TR j, β T j and β j reresent artcle coalescence rate due to turbulent random collson, shear collson n turbulent eddes and tokes buoyancy collson resectvely, and Wall, IF, BIB, BIR, BI and Wake reresent the mass source terms of artcle removal due to wall adheson, artcle own floatng near slag metal nterface, bubble artcle buoyancy collson, bubble artcle turbulence random collson, bubble artcle turbulent shear collson and bubble wake cature resectvely. The detaled exressons for artcle coalescence and removal rate due to these mechansms have been studed and descrbed n our latest ublcaton 17) and wll not be reroduced here Mult nterface and Mult comonent multaneous Reacton Model (RM) In the bottom owder njecton rocess, as shown n Fg. 2. there are four man chemcal reacton laces n ladle, namely to slag lqud steel nterface, ar lqud steel nterface n slag eyes, dserson owder drolet lqud steel nterface and bubble lqud steel nterface, resectvely, and the mult comonent reactons ncludng Al,,, Mn, Fe and O are smultaneously nvolved n each nterface To lag Lqud teel Interface Reactons In the bottom owder njecton rocess n ladle, the to slag lqud steel reacton s one of man chemcal reacton lace, and has an mortant contrbuton on the desulfurzaton effcency. At to slag lqud steel nterface, the multle reactons nvolvng [Al], [], [Mn], [Fe], [O] and [] are consdered to occur smultaneously, and the reacton rate of seces can be wrtten as lslag Acell l lk eff, % Y 100Vcell % Y... (6) L where, s the seces element n lqud steel, namely,, Al,, Mn and Fe. k eff, characterzes the overall mass transfer coeffcent of seces from steel to slag. A cell and V cell are the local nterface area and volume of cell on the lqud steel surface, resectvely. L s nterfacal dstrbuton rato of element at equlbrum, whch reresents thermodynamcs caacty of slag metal reacton and s a functon of oxygen actvty a O *. In order to close the equaton, oxygen knetc balance equaton of slag metal reactons must be solved wth a numercal teraton technque. lslag lslag lslag lslag Al Mn FeO M M M M M Al Mn FeO l slag lslag O... (7) M where, M s the molecular weght of seces n lqud steel and slag. The detaled descrton of thermodynamc and knetc arameters mentoned above n Eqs. (6) and (7) have been clarfed n our revous work. 14) Ar Lqud teel Interface Reactons When lqud steel contacted wth ar at hgher temerature, the oxygen would be absorbed from atmoshere nto steel, and some elements n lqud steel would be oxdzed by dssolved oxygen. These oxdaton reactons rate of seces n slag eyes could be wrtten as A l ar cell km, l l % Y% Y... (8) 100 Vcell where, s Al,, Mn, Fe and C n lqud steel. k m, s the mass transfer coeffcent of seces n lqud steel, and [%Y ] * s the equlbrum concentraton of seces at ar lqud steel nterface. In order to close the equaton, the oxygen mass balance and carbon mass balance equatons must be solved wth a numercal teraton technque. The detaled descrton of these arameters have been clarfed n our revous work. 14) Powder Drolet Lqud teel Interface Reacton Comared wth the to slag lqud steel reacton, the reacton rates of these fne owder drolets are more rad due to the sueror dynamc condtons, and the sulfur concentraton n these drolets would quckly ncrease to the saturaton state. Then the sold hase of Ca would be roduced, and the related thermodynamcs and knetcs of desulhurzaton would vary, whch n turn affect the desulhurzaton rate of owder. Based on the lterature measured date, 18,19) the solublty of Ca n the lqud slag can be aroxmated as N Ca, sat NCaO 333. % NAl 2 O %... (9) where, N Ca,sat s the molar saturaton concentraton of Ca n drolet. N CaO and N Al2O3 reresent the molar concentraton of CaO and Al 2 O 3 n owder drolet, resectvely. Deendng on whether the molar concentraton of Ca O 2018 IIJ 2044

4 IIJ Internatonal, Vol. 58 (2018), No. 11 n owder drolet reaches saturaton, the owder drolet lqud steel nterface reactons can be dvded nto the followng two categores: (1) Unsaturated state,.e. N Ca N Ca,sat Before the molar concentraton of CaO reaches saturaton state, the reacton rate of seces at the owder drolet lqud steel nterface can be wrtten as l l 6 l lk eff, % Y 100d % Y l L... (10) where, s the seces element nvolved reactons, namely, Al,, Mn, and Fe. [%Y ] and (%Y ) are the local mass fracton of seces n lqud steel and owder drolet, resectvely. d s the dameter of owder drolet, and k eff, characterzes the overall mass transfer coeffcent of seces from steel to owder drolet. In Eq. (10), L s the nterfacal dstrbuton rato of each element between drolet and lqud steel, whch reresents thermodynamcs caacty of owder drolet lqud steel reacton and can be exressed as a functon of the nterfacal oxygen actvty a O, l at the owder drolet lqud steel nterface. mlar to the revous arameter, a O, l must also be obtaned by solvng the oxygen knetc balance Eq. (11) of owder drolet lqud steel reactons wth a numercal teraton technque. l l l l l l Al Mn FeO O (11) M M M M M M O Al Mn (2) aturated tate,.e. N Ca > N Ca,sat In the rocess of bottom owder njecton, once the Ca concentraton n owder drolet reaches the saturaton, the sold hase of Ca would be roduced, and the related desulfurzaton rate after sulfur saturated n drolet could be wrtten as FeO 6 k % Y % Y... (12) l 100d l l l m l s s where %Y l s the nterface equlbrum concentraton of element at the lqud surface, whch can be exressed as a functon of a O, l. The related exressons are as follows ao, l %Y... (13) l K f a CaO Therefore, usng Eqs. (11) through (13), the oxygen actvty at the drolet lqud steel nterface can be obtaned for the saturated state of Ca n drolet, whch n turn can gve l the reacton rate of each element Bubble Lqud teel Interface Reacton In bubbly lume flow zone, a large amount of owder artcles wll be adhered to bubble surface, and become an ntegral art of the bubble, as shown n Fg. 2. Wth the bubbles floatng, these owder drolets would also contact and react wth the lqud steel at the bubble lqud steel nterface. mlar to the owder drolet lqud steel nterface reacton, the bubble lqud steel nterface reacton can also be dvded nto the two categores deendng on whether the molar concentraton of CaO reach saturaton n owder drolet adhered on bubble. (1) Unsaturated state,.e. NCa N g Ca,sat g Before the molar concentraton of CaO reaches saturaton state, the reacton rate of seces at the bubble lqud steel nterface can be wrtten as k l b lb l l eff, Y f % Ar g 6 g g1 100 % Y % Y greal, lb 100 d L... (14) where, f reresents the rato of the effectve contact area between adhered drolet and lqud steel. In ths aer, f was unformly set to 0.5. ρ g s the densty of bubble after adherng owder artcles and could be calculated usng the followng exresson. g g g 1 % YAr % YAr Ar... (15) b In Eq. (14), L s the nterfacal dstrbuton rato of each element between bubble and lqud steel, and can be exressed as a functon of the nterfacal oxygen actvty a O, l-b, whch must be obtaned by solvng the followng oxygen knetc balance of bubble metal reactons wth a numercal teraton technque. l b l b l b l b l b l b Al Mn FeO O (16) M M M M M M O Al Mn (2) aturated state.e. NCa N g Ca,sat g In the bubble lqud steel reacton rocess, once the roduct Ca concentraton n owder drolet whch was adhered on bubble reaches the saturaton, the sold hase of Ca would be roduced, and the desulfurzaton rate can be exressed by the followng exresson. f % Y Ar g 6 g g1 100 lb l lk m, % Y % Y lb 100 d... (17) FeO where, %Y l b s the equlbrum concentraton of sulfur at the bubble lqud nterface, whch can be exressed as a functon of a O, l-b ao %Y... (18) lb KfaCaO,g Therefore, usng Eqs. (16) through (18), the oxygen actvty at the bubble lqud steel nterface can be obtaned for the saturated state of Ca, whch n turn can gve the reacton rate of each element b l Numercal cheme In the resent work, the CFD PBM RM couled model was solved usng the commercal comutatonal flud dynamcs software fluent 12.0 combned wth User Defned Functon (UDF), to descrbe the multhase transort behavor and reacton knetcs n 80-ton ladle wth bottom owder njecton, and the dual slot lugs were laced symmetrcally IIJ

5 IIJ Internatonal, Vol. 58 (2018), No. 11 at 0.5R from the bottom center (R s the bottom radus of the ladle). Fgure 4 shows the mesh of 80-ton ladle used n the resent model, and the dmensons of ladle and other arameters are lsted n Table 1. Due to the symmetry of the flow, only half of the geometrc model was bult as comutatonal doman, and the mesh consstng control volumes was used. The bottom and sde walls were set as no sl sold walls, and the standard wall functon was used to model the turbulence characterstc n the near wall regon. The velocty nlet was used for gas blowng and owder njecton at the bottom tuyeres, and a flat surface was assumed at the to surface. In resent work, the ntal velocty of owder artcle was assumed to the same as the gas velocty at bottom slot, and the rsng velocty of owder s obtaned by solvng the momentum conservaton equaton, whch consdered the drag force and turbulent dserson force among three hases as momentum exchange source terms. The tycal workng condtons of actual ladle desulfurzaton, was as an ntal condton for bottom owder njecton rocess n 80-ton ladle, and the chemcal comostons of lqud steel, to slags and owders were gven n Tables 2 and 3. Fg. 4. The mesh of 80-ton ladle used n resent model. (Onlne verson n color.) Table 1. The dmensons of 80-ton ladle and other arameters emloyed n model. Dameter of ladle (u) Dameter of ladle (down) Heght of ladle Argon gas flow rate Powder njecton rate Thckness of slag mm mm mm 200 to 800 NL/mn 3 to12 kg/mn 95 mm Densty of lqud steel kg/m 3 Densty of slag kg/m 3 Densty of gas kg/m 3 Molecular vscosty of molten steel Pa s 3. Results and Dscusson In the bottom owder njecton rocess, the multhase flow transort and chemcal reactons behavor affect sgnfcantly desulfurzaton effcency and effectveness, and need to be accurately descrbed and redcted. In our revous work, 14 17) by the CFD model, the redcted bubbly lume flow ncludng gas volume fracton, lqud velocty and turbulent knetc energy had been valdated aganst exermental data, 16) and by the CFD RM couled model, the redcted multcomonent smultaneous reacton at to slag lqud steel nterfacal n ladle agrees well wth the measured data. 14,15) In our latest lterature, 17) a CFD PBM RM coule model had been develoed to descrbe the multhase flow and reacton knetc n the bottom owder njecton rocess. Model valdaton was carred out usng hot tests n 2 ton nducton furnace wth bottom owder njecton, and the redcted sulfur content n 2 ton furnace agreed well wth the measured data. In resent work, the CFD PBM RM couled model was used to redct desulfurzaton effcency n 80 ton ladle wth bottom owder njecton. The reacton rate and evoluton of multle nterhase reactons nvolvng dealumnaton, deslcaton, demanganzaton and desulfurzaton were revealed. The effects of dfferent knetc condtons on the desulfurzaton effcency were nvestgated, and the mortance of varous reacton mechansms was dscussed and clarfed Multle Interface Reactons Knetcs In the bottom owder njecton rocess, as shown n Fg. 2, there are four man chemcal reacton stes n ladle, namely to slag lqud steel nterface, ar lqud steel nterface n slag eye, dserson owder artcle lqud steel nterface and bubble lqud steel nterface, resectvely, and n these nterfaces, the mult comonent reactons ncludng Al,,, Mn, Fe and O would occur smultaneously and mact wth each other Powder Partcle lqud teel Interface Reacton Fgure 5 shows the redcted mole reacton rates of dfferent seces at the owder artcle lqud steel nterface n 10 mn after the start of bottom owder njecton. The ntal comonent concentraton of lqud steel, to slag and owder were gven n Tables 2 and 3. The gas flow rate s 600 NL/mn, and the owder njecton rate s 6 kg/mn. n reresents the reacton mole rate of seces at the owder artcle lqud steel nterface, whch can be exressed as Table 3. Chemcal comoston of owder njected n 80-ton ladle. (Al 2O 3) (O 2) (CaO) () (CaF) (FeO) (MnO) 21.32% 6.12% 57.62% 0.08% 13.07% 1.23% 0.12% Table 2. Intal chemcal comoston of slag and lqud steel n 80-ton ladle. Comoston n steel (%) Comoston n slag (%) Temerature (K) [Al] [] [Mn] [C] [] (Al 2O 3) (O 2) (CaO) (MnO) () (FeO) (MgO) IIJ 2046

6 IIJ Internatonal, Vol. 58 (2018), No. 11 Fg. 5. Predcted the reacton mole rates of dfferent seces at the owder metal nterface: (a) n Al, (b) n, (c) n Fe, (d) n Mn, (e) n, melt, (f) n, sold. (Onlne verson n color.) Fg. 6. Predcted the contour ma of (a) CaO molar concentraton, (b) Al 2O 3 molar concentraton, and (c) Ca saturaton molar concentraton n owder drolet. (Onlne verson n color.) n l M... (19) where, s the mass source of seces due to owder artcle lqud steel nterface reacton, M s the molecular weght of seces. From Fg. 5, t can be seen that n l Al s ostve n bubbly lume zone, whch ndcate [Al] would be removed from lqud steel nto owder drolets due to the reacton at the owder lqud steel nterface. multaneously, n l and n l Fe are negatve, whch ndcate that the (O 2 ) and (FeO) would be reduced by [Al] from owder drolets nto lqud steel. Furthermore, t can be also found that as the owder drolets floatng u, the reacton mole rates decrease because each comonent s gradually close to the equlbrum state. However, n the vcnty of the lqud surface, the reacton rate suddenly ncreases, ths s because that the owder artcles adhered on bubble would return to the lqud steel wth the ruture of the bubbles n the slag eye zone, and the comonents n these artcles are stll not reached an equlbrum state and n turn react ntensely wth the lqud steel. In Fgs. 5(e) and 5(f), n, melt and n, sold reresent the desulfurzaton mole rates when the desulfurzaton roducts Ca are lqud hase and sold hase, resectvely. It should be noted that n the vcnty of bottom slot lugs, the desulfurzaton roducts Ca s lqud hase, whle n the uer regon of the ladle, the desulfurzaton roducts Ca 2047 s sold hase. Ths s manly because as the refnng owder s njected nto lqud steel, the chemcal reactons would strongly take lace between fne owder drolet and lqud steel, and the lqud roduct Ca and Al 2 O 3 concentraton would radly ncrease, whle the CaO concentraton would decrease, as seen n Fg. 6. Accordng to the Eq. (9) summarzed from the lterature measure, 17,18) the solublty of Ca n owder drolet would decrease radly wth these drolets floatng, as seen n Fg. 6(c). Once the sulhur reaches saturaton,.e. N Ca > N Ca,sat, the sold hase of Ca would be roduced, and the related thermodynamcs and knetcs of desulhurzaton would vared, whch n turn reduce the desulhurzaton rate of owder. Fgure 7 gves the redcted the change of seces reacton molar rate at the owder artcle lqud steel nterface wth tme n 80-ton ladle wth bottom owder njecton. The owder njecton rate s 6 kg/mn and the gas flow rate s 600 NL/mn. From ths fgure, t can be found that the dealumnaton rate n l Al and desulfurzaton rate n, sold are obvously larger than other reacton rates. Ths s because that ntal comonents [Al] was manly consumed to roduce lower nterfacal oxygen otental and romotes the desulfurzaton reacton. multaneously, the redundant [Al] n lqud steel would be consumed to romote the reducton rate of (O 2 ) and (FeO). These reactons can be manly exressed as [Al] [] CaO Ca AlO sold (20), 2018 IIJ

7 IIJ Internatonal, Vol. 58 (2018), No. 11 [Al] [] CaO Ca AlO melt (21), [Al] O AlO 2 3 [Al] FeO Fe AlO... (22)... (23) Furthermore, t can also be observed that wth the owder njecton tme, these reacton rates gradually decreased, and n l Mn s ostve but very small, because ts ntal concentraton n the owder drolet s very low and close to the nterfacal equlbrum concentraton Bubble lqud teel Interface Reacton In bubbly lume flow zone, a large amount of owder artcles wll be adhered to bubble surface. Wth the bubbles floatng, these adhered artcles would also contact and react wth the molten steel, and ther dynamcs condton are qute dfferent from that of dserson owders n lqud steel. Therefore, the reacton behavor between artcles adsorbed on bubble and lqud steel need to be consdered searately. Fgure 8 shows the redcted dfferent seces reacton molar rates at the bubble lqud steel nterface n 10 mn after the start of bottom owder njecton n 80-ton ladle, and Fg. 9 gves the curve change of dfferent seces reacton molar rate at the bubble lqud nterface wth tme. In these fgures, the gas flow rate s 600 NL/mn, the owder b njecton rate s 6 kg/mn. n reresents the reacton mole rate of seces at the bubble lqud steel nterface, whch can be exressed as n l b l b... (24) M b where s the mass source of seces due to owder artcle lqud steel nterface reacton. It can be found from these fgures that smlar to the owder drolet lqud steel nterface reactons, the n l Al b l b and n, sold are greater than the other reacton rates, and n the lower regon of bubbly lume zone, the desulfurzaton roducts Ca was lqud hase, whle n the uer regon of bubbly lume zone, the desulfurzaton roducts Ca was sold hase. Furthermore, comared wth the owder artcle lqud steel nterface reactons, the bubble lqud steel nterface reacton rate s obvously smaller because the contact secfc surface and tme between bubble and lqud steel are far lower than that between the dserson artcles and lqud steel. Fg. 7. Predcted the change of seces reacton molar rate at the owder metal nterface wth tme n 80-ton ladle. (Onlne verson n color.) Fg. 9. Predcted the change of seces reacton molar rate at the bubble metal nterface wth tme n 80-ton ladle wth bottom owder njecton. (Onlne verson n color.) Fg. 8. Predcted the seces reacton molar rate at the bubble metal nterface: (a) nal b, (b) n b, (c) nfe b, (d) nmn b, (e) l b n, l b melt, (f) n, sold. (Onlne verson n color.) 2018 IIJ 2048

8 IIJ Internatonal, Vol. 58 (2018), No To lag Lqud teel and Ar Lqud teel Interface Reactons In ladle, the to slag s ushed to the erhery of a ladle by the acton of nert gas bubblng to form slag eyes, where the lqud steel s drectly exosed to the ambent envronment. Therefore, on the lqud steel to surface, there are two man reacton stes, namely the to slag lqud steel nterface and ar lqud steel nterface. Fgure 10 shows the redcted reacton molar rates of dfferent seces at the to slag lqud steel nterface and ar lqud steel nterface n 10 mn after the start of bottom owder njecton n 80-ton ladle. Fgure 11 gves the curves changes of reacton molar rates of dfferent seces wth tme. In these fgures, the gas flow rate s 600 NL/mn and to the owder njecton rate s 6 kg/mn. n reresents the reacton mole rate of seces on the lqud steel to surface, whch can be exressed as n lto M l to lslag l ar... (25) M slag ar where, and reresents the mass source of seces due to to slag lqud steel nterface and ar lqud steel nterface reactons, resectvely. As shown n Fg. 10, n slag eyes, the l to Al and l to are negatve, whle l to Mn, l to Fe and l to are almost zero. Ths s because the oxygen would be absorbed from atmoshere nto lqud steel, and the alumnum and slcon would be referentally oxdzed by dssolved oxygen due to ther strong reducblty n lqud steel. At the to slag lqud steel nterface, the and Fe become ostve, because dealumnaton reacton occurs at the slag lqud steel nterface and lowers the oxygen otental, whch n turn romote the desulfurzaton reacton and the reducton reacton of (O 2 ) and (FeO) n to slag. Furthermore, t can be also observed that these knetc reacton absolute rates are large near the slag eye zone and decrease along the radal. Fgure 11 llustrates the change of seces reacton molar rate at the to slag metal nterface and ar metal nterface wth tme n 80-ton ladle wth bottom owder njecton. From ths fgure, t can be seen that at the ntal moment, the ntense dealumnaton and demanganzaton reactons romote the desulfurzaton reacton and the reducton reacton of (O 2 ) and (FeO). Wth the owder njecton tme ncreasng, these reacton rates gradually decreased because each comonent s gradually close to the equlbrum state. Furthermore, t needs to be notced that the net reacton rate of [] n lqud steel s very small, ths s because the consumton rate of slcon due to beng oxdzed from lqud steel n slag eyes zones, s almost equal to the generaton rate due to the reducton reacton of (O 2 ) from to slag nto lqud steel at the to slag lqud steel nterface, as shown n Fg. 11(b) ulfur Local Dstrbuton and Desulfurzaton Effcency ulfur Local Mass Dstrbuton n Ladle In ladle bottom owder njecton rocess, the seces n lqud steel can be transferred by molecular dffuson and lqud turbulent flow, and they can be also roduced nto or removal from lqud steel due to the chemcal reacton at owder lqud steel nterface, bubble lqud steel nterface, to slag lqud steel nterface and ar lqud steel nterface. Fg. 11. Predcted the change of reacton molar rate of dfferent seces at the to slag metal nterface and ar metal nterface wth tme n 80-ton ladle. (Onlne verson n color.) Fg. 10. Predcted the contour ma of dfferent seces reacton molar rate at the slag metal nterface and ar metal nterface: (a) n l to, (b) n l to, (c) n l to, (d) n l to, (e) n l to. (Onlne verson n color.) Al Mn Fe IIJ

9 IIJ Internatonal, Vol. 58 (2018), No. 11 Fgure 12 shows the tycal local dstrbuton of sulfur content n ladle n 1 mn, 10 mn and 20 mnutes after the start of bottom owder njecton. The gas flow rate s 600 NL/mn, the owder njecton rate s 6 kg/mn, and the ntal comonent concentraton of lqud steel, to slag and owder artcle were gven n Tables 2 and 3. From ths fgure, t can be found that the sulfur content has the lowest value n the vcnty of bottom slot lugs, and then gradually ncreases wth the ung lqud steel flow due to contnuous mxng wth surroundng lqud steel flow wth hgh sulfur concentraton. When the ung lqud steel flow reaches the to lqud surface, the sulfur content would gradually decrease along the drecton of lqud steel flow due to the to slag lqud steel reacton, and fnally the lqud steel surface stream would be re mxed nto the ladle nteror along the sde wall and the two bubblng flows. Thus, such a rocess s formed n the whole ladle to transfer and removal sulfur wth tme, as shown n Fgs. 12(b) and 12(c). Fgure 13 shows the change of redcted sulfur mass average content and desulfurzaton rato wth tme n 80-ton ladle. In the current work, the φ s roosed to reresent the l total desulfurzaton rato, l, b lto and are desulfurzaton sub rato attrbuted by owder artcle lqud steel nterface reacton, bubble lqud steel nterface reacton and to slag lqud steel nterface, resectvely. From ths fgure, t can be found that wth the ncrease of owder njecton tme, the average sulfur concentraton [] n the lqud steel decreases from to , and the fnal total desulfurzaton rato φ s 72.3%. For the three man desulfurzaton mechansms, the contrbuton of the owder lqud steel nterface reacton s the largest, whch s 45.01%, and then followed by the to slag lqud steel nterface desulfurzaton wth 19.42%, whle the contrbuton of bubble lqud steel nterface desulfurzaton s the smallest Effect of Gas Flow Rate Fgure 14 gves the effect of gas flow rate on the redcted desulfurzaton rato due to varous reacton mechansms n 80-ton ladle wth bottom owder njecton. The owder njecton rate s 6 kg/mn, and the ntal comonent concentraton of lqud steel, to slag and owder artcle are gven n Tables 2 and 3. From ths fgure, t should be stated that wth the gas flow rate ncreasng from 200 NL/ mn to 800 NL/mn, the fnal average sulfur concentraton n lqud steel ncreases from to ,.e. the desulfurzaton rato φ wll decrease from 72.3% to 63.9%. Ths s because, as the gas flow rate ncreases, the rate of owder bubble collson and adheson ncrease. The dserson artcle lqud steel nterface desulfurzaton l rato would quckly decrease, whle the growth rate of lb bubble lqud steel nterface desulfurzaton rato s relatvely slow due to the lower contact secfc surface and tme between bubble and lqud steel Effect of Powder Injecton Rate Fgure 15 shows the effect of owder njecton rate on the redcted desulfurzaton rato due to varous reacton mechansms n 80-ton ladle wth bottom owder njecton. The gas flow rate s 600 NL/mn, and the ntal comoston of lqud molten steel, to slag and owders s shown n Tables 2 and 3. From ths fgure, t can be found that when the bottom owder njecton amount s 0.75 kg/t,.e. the owder njecton rate and tme s 3 kg/mn and 20 mn, the desulfurzaton rato φ s only 51.9%, and the to slag lqud steel nterface reacton s the domnant desulfurzaton mechansm. Wth the ncreases of owder njecton rate from 0.75 kg/ton to 3 kg/ton, the desulfurzaton rato φ quckly ncreases from 51.9% to 82.5%, and the contrbuton of owder lqud steel nterface reacton and Fg. 12. Predcted local dstrbuton of the sulfur content n (a) 60 s, (b) 600 s and (d) s after the start of bottom owder njecton n 80-ton ladle. (Onlne verson n color.) Fg. 13. Predcted (a) the sulfur mass content, and (b) desulfurzaton rato due to varous reacton mechansms wth tme n 80-ton ladle wth bottom owder njecton. (Onlne verson n color.) 2018 IIJ 2050

10 IIJ Internatonal, Vol. 58 (2018), No. 11 Fg. 14. Effect of gas flow rate on the redcted (a) sulfur mass content, and (b) desulfurzaton rato due to varous reacton mechansms n 80-ton ladle. (Onlne verson n color.) Fg. 15. Effect of owder njecton rate on the redcted (a) sulfur mass content, and (b) desulfurzaton rato due to varous reacton mechansms n 80-ton ladle. (Onlne verson n color.) bubble lqud steel nterface reacton ncrease and become the domnant desulfurzaton mechansms, whle the role of the to slag lqud steel reacton s gradually weakened. 4. Conclusons The CFD PBM RM couled model was used to redct the multhase flow behavor and reacton knetc n 80 ton ladle wth bottom owder njecton. The reacton rate and evoluton of mult-comonents ncludng Al,,, Mn and Fe at the owder drolet lqud steel nterface, bubble lqud steel nterface, to slag lqud steel nterface and ar lqud steel nterface were revealed, and the mortance of varous mechansms was dscussed and clarfed. At the lower owder njecton rate, the desulfurzaton s manly attrbuted to the jont effort of both owder lqud steel reacton and to slag lqud steel reacton whch s the revalng mechansm. At the hgher owder njecton rate, the owder lqud steel and bubble lqud steel nterface reacton becomes more mortant and then redomnates the desulfurzaton behavor. Wth the ncreasng of gas flow rate, the total desulfurzaton rato φ gradually decreases, and wth the ncrease of owder njecton rate, the total desulfurzaton rato φ ncrease. As the gas flow rate s 600 NL/mn, wth the owder njecton rate ncreasng from 0.75 kg/t to 3 kg/t, the φ ncreases from 51.9% to 82.5%. Acknowledgment The authors wsh to exress thanks to the Natonal Natu- ral cence Foundaton of Chna ( ) and Natonal Key R&D Program of Chna (2017YFC ) for suortng ths work. REFERENCE 1) M. Y. Zhu, J. A. Zhou,.. Pan and J. ha: Technology and Devce for Bottom Powder Injecton through lot Brck n Ladle, Chnese Patent CN , (2006). 2) M. Y. Zhu and Z. F. Chen: A Devce for Bottom Powder Injecton through Plunge-slot and Ant-blockng Brck n Ladle, Chnese Patent CN , (2013). 3) M. Y. Zhu, Z. F. Chen and W. T. Lou: A Devce for RH Vacuum Refnng wth Bottom Powder Injecton, Chnese Patent CN , (2014). 4) M. Y. Zhu, Z. F. Chen and W. T. Lou: A Devce and Method for Vacuum Degassng Refnng of Molten teel wth Bottom Powder Injecton, Chnese Patent CN , (2014). 5) Z. F. Chen and M. Y. Zhu: Metall. Mater. Trans. B, 45B (2014), ) P. K. Iwamasa and R. J. Fruehan: Metall. Mater. Trans. B, 28B (1997), 47. 7) D. R. Roy, P. C. Pstorus and R. J. Fruehan: Metall. Mater. Trans. B, 44B (2013), ) D. R. Roy, P. C. Pstorus and R. J. Fruehan: Metall. Mater. Trans. B, 44B (2013), ) E. hbata, H. P. un and K. Mor: Metall. Mater. Trans. B, 30B (1999), ) M. Reffersched and W. Pluschkell: teel Res., 65 (1994), ) M. Andersson, M. Hallberg, L. Jonsson and P. Jönsson: Ironmakng teelmakng, 29 (2002), ) L. Jonsson,. C. Du and P. Jönsson: IIJ Int., 38 (1998), ) M. A. T. Andersson, L. T. I. Jonsson and P. G. P. Jönsson: IIJ Int., 40 (2000), ) W. T. Lou and M. Y. Zhu: Metall. Mater. Trans. B, 45B (2014), ) W. T. Lou and M. Y. Zhu: IIJ Int., 55 (2015), ) W. T. Lou and M. Y. Zhu: Metall. Mater. Trans. B, 48B (2017), ) W. T. Lou and M. Y. Zhu: Metall. Mater. Trans. B, 44B (2013), ) B. Y. hro, H. Makoto, K. Tetsuro and M. Hno: IIJ Int., 44 (2004), ) J. X. Cheng: The Common Use Handbook of Dagram for teelmakng, Metallurgcal Industry Press, Bejng, (2010), IIJ