FLUID FLOW AND INCLUSION REMOVAL IN MOLTEN STEEL CONTINUOUS CASTING STRANDS

Ffth Internatonal Conference on CFD n the Process Industres CSIRO, Melbourne, Australa 1-15 December 006 FLUID FLOW AND INCLUSION REMOVAL IN MOLTEN STEEL CONTINUOUS CASTING STRANDS Lfeng ZHANG Professor, Det. of Materals Scence & Engneerng, Norwegan Unversty of Scence & Technology (NTNU) Alfred Getz ve, N-7491 Trondhem, Norway, Emal: lfeng.zhang@materal.ntnu.no htt://www.nt.ntnu.no/users/lfengz/ ASTRACT Turbulent flow, the transort of nclusons and bubbles, and ncluson removal by flud flow transort and by bubble flotaton n the strand of the contnuous slab caster are nvestgated usng comutatonal models, and valdated through comarson wth lant measurements of nclusons. Steady -D flow of steel n the lqud ool n the mold and uer strand s smulated wth a fntedfference comutatonal model usng the standard k-ε turbulence model. Traectores of nclusons and bubbles are calculated by ntegratng each local velocty, consderng ts drag and buoyancy forces. A random walk model s used to ncororate the effect of turbulent fluctuatons on the artcle moton. The attachment robablty of nclusons on a bubble surface s nvestgated based on fundamental flud flow smulatons, ncororatng the turbulent ncluson traectory and sldng tme of each ndvdual ncluson along the bubble surface as a functon of artcle and bubble sze. The change n ncluson dstrbuton due to removal by bubble transort n the mold s calculated based on the comuted attachment robablty of ncluson on each bubble and the comuted ath length of the bubbles. Results ndcate that 6-10% nclusons are removed by flud flow transort, 10% by bubble flotaton, and 4% by entrament to the SEN walls. Smaller bubbles and larger nclusons have larger attachment robabltes. Smaller bubbles are more effcent at ncluson removal by bubble flotaton, so long as they are not entraed n the soldfyng shell. Larger gas flow rate favors ncluson removal by bubble flotaton. The otmum bubble sze should be -4mm. INTRODUCTION Increasng the roductvty and mrovng the roduct qualty are ermanent requrements concernng the contnuous castng rocess. To roduce clean steel wth as few nclusons as ossble s one of the man tasks of steelmakers. Inclusons can be removed from the molten steel by flud flow transort or by bubble flotaton 1-6). Inclusons attached to the surface of bubbles can be removed faster due to the small resdence tme of bubbles n the molten steel. However, bubbles wth attached nclusons can fnally generate lne defects such as blsters and encl es f they are entraed to the soldfed shell. 7, 8) Fgure 1 s the examle of bubbles wth attached nclusons 9, 10). Plant observatons have found that many serous qualty roblems, ncludng ncluson entrament, are drectly assocated wth the flow attern n the mold. 11) Thus desgn and control of the flud flow attern n the contnuous castng mold to remove nclusons s of crucal mortance to the steel ndustry. The flow attern n the mold can be controlled by many varables, ncludng the nozzle and mold geometry, submergence deth, steel flow rate, argon necton rate, electromagnetc strrng, and flux layer roertes. Nozzle technology s an easy and nexensve way to otmze the flud flow n the mold. New technques nvolvng the Submergence Entry Nozzle (SEN) to mrove the flud flow attern and ncluson removal ncludes swrl nozzle technque 1-15), ste nozzle technque 16-0), multorts nozzle 1), and oval offset bore throttle late, ). The flud flow n the contnuous castng mold can be nvestgated by mathematcal modelng 4-9), hyscal modelng 0-9), or ndustral trals 40-4). Mathematcal modelng s an effectve, nexensve tool to get nformaton that cannot be drectly measured n the steel. In the current study, ndustral measurement of nclusons and total oxygen n a Low Carbon Al-klled steel are measured. The steady flow n the SEN and the strand of the contnuous caster s smulated wth a -D fntedfference comutatonal model usng the standard k-ε turbulence model n Fluent 4). Incluson traectores are calculated by ntegratng each local velocty, consderng ts drag and buoyancy forces. A random walk model s used to ncororate the effect of turbulent fluctuatons on the artcle moton. Fgure1. Inclusons attached on bubbles n a CC slab 10) 1

MATHEMATICAL MODEL OF FLUID FLOW AND INCLUSION MOTION Mathematcal Models- Modulaton The contnuty equaton and Naver-Stokes equatons for the steady flud flow of ncomressble Newtonan fluds are ( ρu ) = 0 (1) P u u ( uu ) ( o t ) ρ = + μ + μ + + ρg + F () x x where ρ, lqud densty (kg/m ); u, velocty comonent n x drecton (m/s); P, ressure feld (N/m ); μ o, lamnar vscosty (kg/m-s); μ t, turbulence vscosty (kg/m-s); g, magntude of gravty n drecton (m/s ); F, other body forces (eg. from eletromagnetc forces);,, coordnate drecton ndces, whch when reeated n a term, mles the summaton of all three ossble terms. Wth the k-ε Model 44), the turbulent vscosty s gven by k μt = ρc, () μ ε where C μ,emrcal constant = 0.09; k, turbulent knetc energy feld, m /s ; ε= turbulent dssaton feld, m /s. The two addtonal artal dfferental equatons for the transort of turbulent knetc energy and ts dssaton rate are gven by: ρu k μ t k v μ u u + +, (4) = ρε σ t x K x x x x ε μ ε ε u u u t ρv = + C μ 1 t + C σ ε K ε, (5) ρε K where /, dfferentaton wth resect to coordnate drecton x,y, or z (m); σ K, σ ε, emrcal constants (1.0, 1.); C 1, C, emrcal constants (1.44, 1.9). The k-ε Model needs secal wall functons as boundary condtons, n order to acheve reasonable accuracy on a coarse grd. 4) The traectory of each artcle can then be calculated ncrementally by ntegratng ts local velocty. The local velocty of nclusons s reresented by Eq.(6) consderng the force balance between drag force and the gravtatonal force. du dt ( ρ ρ ) 1 ρ (6) = CD ( u u ) g 4 d ρ ρ where ρ P and ρ, the artcle and lqud denstes, kg/m ; u,, the artcle velocty, m/s; C D, the drag coeffcent as a functon of artcle Reynolds number, gven as below 4 C D = + Re ( 1 0.186 Re 0.65 ). (7) A random walk model s used to ncororate the effect of turbulent fluctuatons on the artcle moton. In ths model, artcle velocty fluctuatons are based on a Gaussan-dstrbuted random number, chosen accordng to the local turbulent knetc energy. The random number s changed, thus roducng a new nstantaneous velocty fluctuaton, at a frequency equal to the characterstc P lfetme of the eddy. The nstantaneous flud velocty can be reresented by u u + u =, (8) u = ξ u = ξ k (9) where u : the nstantaneous flud velocty, m/s; u : the mean flud hase velocty, m/s; u : random velocty fluctuaton, m/s; ξ: the random number. As boundary condtons for the artcle moton, artcles escae at the to surface and the oen bottom, are reflected at symmetry lane, and are entraed when they touch wde faces and narrow faces whch reresent the dendrtc soldfcaton front.. Ths trang boundary condton s vald for artcles smaller than the rmary dendrte arm sacng and has been emloyed by several researchers 45-47). However, artcles touchng the soldfyng front are not always engulfed. The entrament henomenon s very comlex and s recevng welldeserved attenton n recent work. 48-50) The arameters of the SEN and the caster are shown n Table 1. SEN Parameters Value SEN bore dameter, length 80, 19 (mm) SEN submergence deth (mm) 00 Port wdth ort heght 65 80 (mm mm) Port thckness (mm) 0 ottom well deth (mm) 10 Mold Parameters Value Nozzle ort angle Down 15o, u 15o, zero Submergence deth (m) 0.05, 0.10, 0.15, 0.0, 0.5, 0. Doman heght/wdth/thckness.55/1./0.5 (m) Castng seed (m/mn).0,1.6,1.,0.8 Partcle dameter (µm) 00, 00, 50, shercal Flud densty (kg/m) 700 Flud knetc vscosty (m/s) 0.954 10-6 Partcle densty (kg/m) 500 Argon bubble densty ( kg/m) 1.68 Argon bubble sze (mm) 1-10 Incluson moton model Random walk, 00 tres, 10000 nclusons Table 1.. Parameters of the SEN and contnuous caster INTERACTION ETWEEN ULE AND INCLUSION IN THE MOLTEN STEEL The attachment rocess of an ncluson to a gas bubble n the molten steel roceeds through the followng stes: The ncluson aroaches the gas bubble. If the lqud thn flm between the artcle and the bubble decreases to less than a crtcal thckness durng the contact tme between the bubble and the ncluson,.e., the sldng tme of the ncluson on the surface of the bubble, t wll suddenly ruture causng the ncluson to attach ermanently to the surface of the bubble. Otherwse, the ncluson wll move away from the bubble. The crtcal flm thckness and flm ruture tme are calculated elsewhere. 1) In order to calculate the nteracton tme and the attachment robablty of nclusons to the bubble surface,

a comutatonal smulaton of turbulent flow around an ndvdual bubble and a smulaton of ncluson transort through the flow feld are requred. Frst, the steady turbulent flud flow of the molten steel around an argon bubble s calculated, assumng ax-symmetry. Possble deformaton of the bubble shae by the flow and ncluson moton s gnored. The far-feld velocty condton s set to be of the bubble termnal velocty, assumng a sutable turbulent energy and dssaton rate, and a far feld ressure outlet. Then the ncluson traectores around the bubble are calculated. Several thousand nclusons are unformly nected nto the doman n the column wth dameter far larger than d +d from the lace of the 15-0 tmes of the bubble dameter far from the bubble center. As boundary condtons, nclusons reflect f they touch the surface of the bubble. If the normal dstance of the ncluson center to the surface of the bubble s frst less than the ncluson radus, the collson between the ncluson and the bubble takes lace. And f ths dstance kees less than the ncluson radus for some tme, then t s the sldng tme. Inclusons wll be attached to the surface of the bubble accordng to the crteron dscussed before. Then the attached robablty, as shown n Fgure, can be exressed by én ù o, PA ( ( R R) R T, ) å å + D - N, (10) ê ú P = = ë û A+ P ( d+ d) 4 where N o s the number of nclusons attachng to the bubble by satsfyng that ther contact tme s larger than the flm ruture tme. A +P s the secton area of the column wth dameter of d +d P. N T, s the total number of nclusons nected through the area A, and s the sequence number of the annular oston at whch the nclusons are nected. - ubbles all have the same sze; - Inclusons have a sze dstrbuton and are unformly dstrbuted n the molten steel, and they are too small to affect bubble moton or the flow attern; - The bubble sze and the gas flow rate are chosen ndeendently; - Once stable attachment occurs between a bubble and an ncluson, there s no detachment and the ncluson s consdered to be removed from the molten steel, owng to the hgh removal fracton of most bubbles. Assumng that all nclusons are Al O, the total oxygen (n m) removed by bubble flotaton can be exressed by n Δ = 5 1 d L ρ ( O 1.16 10 n ) PA d (11), V S t = 1,, ρ n n, = n, 1 C = QGT 7π ( 100 P ) M 100 t d A M π d L 4 VC S t 60 (1) (1) where d s the bubble dameter (m), L s the ath length of the bubble (m), t s the bubble resdence tme (s), P A s the attachment robablty of the ncluson to the bubble (%), and n s the number densty of that ncluson sze (number/m steel), V C s castng seed (m/mn), S s the area of the slab secton (=0.5 1.m ), ρ and ρ M are denstes of nclusons and the molten steel. n s the number of bubbles n the doman durng tme t, Q G s the gas flow (Nl/mn), T M s the steel temerature (18K). n, s the number densty of ncluson wth dameter d, when bubble s nected, used to udate the ncluson number densty dstrbuton after the calculaton of each ndvdual bubble n order to account for the sgnfcant change n ncluson concentraton caused by the smultaneous ncluson removal of many bubbles. FLUID FLOW AND INCLUSION MOTION IN SEN REGION bubble d b R R +ΔR Fgure. Schematc of the attachment robablty of nclusons to the bubble surface under stochastc turbulent effect A removal model of nclusons by bubble flotaton s develoed for the molten steel-alumna nclusons-argon bubbles system. The followng assumtons are used: d The smulaton doman s shown n Fgure. In the current smulaton, the SEN and the mold s combned together. The effect of annular stes on the flud flow and ncluson moton n the SEN and caster strand are nvestgated. Two annular stes n a SEN (Ste SEN) s calculated. Due to the shar decreasng of the bore dameter at the stes, the flud flow s accelerated at these locatons n the Ste SEN. Ths acceleraton hels to dmnsh the non-unform veloctes generated by the slde gate. Near the slde gate, nclusons may have slght recrculaton, as shown n Fgure. Wthout stes, the uneven flow assng the slde gate fnally generates a swrl at the bottom of the nozzle, therefore the molten steel enters mold wth swrl, as shown n Fgure and Fgure 4. Ths swrl at the bottom and outorts are dmnshed n the Ste SEN. Jet characterstcs for nozzles wth outorts angle of 15 o down, 0 o horzontal, 15 o u, and Stes are comared n Table. The 15 o down nozzle wth two stes has the smallest turbulent energy and dssaton rate, whch means the et enterng the mold has the weakest turbulence. The et angle s only 18 o for the Ste SEN (Down 15 o ), comared wth 9 o wthout stes (Down15 o ),

and 18 o for Zero degree angle nozzle wthout Stes. The large et angle corresonds to a large mngement deth, therefore worsens the ncluson removal to the to surface. One roblem of the Ste SEN s ts large back flow zone fracton, 0%, comared wth all three conventonal nozzles n Table. Larger back-flow zone wll brng more nclusons back to the outort regon of SEN, ossbly nducng cloggng there. The ste nozzle may have more ncluson removal to the to surface of the mold erhas by elmnatng swrls at SEN outorts and n the mold, and by deceasng the mngement deth of the et n the mold. For the down 15 o angle nozzle, only 17% of the 50µm nclusons are removed to the to surface, but ths number ncreases to 1% wth two annular stes, as shown n fgure 5. Zero angle nozzle and u 15 o nozzle have a slght larger ncluson removal fracton to the to, ~0-%. ecause the ncluson removal rates are so small for all nozzles, t s more mortant to choose nozzle desgns that roduce otmal condtons at the menscus to avod slag entranment, level fluctuatons, and other roblems. Fgure. Smulaton doman (left), swrl athlne at the outort of SEN (mddle), and ncluson traectores near the slde gate SEN Outort angle Down15 Down 15 Zero U 15 Wth stes or not No Stes No No Weght mean x velocty (m/s) 0.80 0.96 0.87 0.86 Weght average y velocty (m/s) -0.051 0.01 0.0018-0.007 Weght average z velocty 0.45 0. 0.14 0.8 (m/s) Weght average turbulent 0.7 0.0 0. 0.1 energy (m /s ) Weght average turbulent 6.41 5.7 10.47 8.88 energy dssaton rate (m /s ) Vertcal et angle ( o ) 9.9 18. 9.10 17.76 Horzontal et angle ( o ) -.5 0.7 0.1-0.47 Jet seed (m/s) 0.9 1.01 0.89 0.90 ack-flow zone fracton (%) 15.1 9.8 6.15 0.7 Swrl or not at Outorts Wth No Wth Wth Table Jet characterstcs of SEN wth dfferent outorts angle and stes n nozzle (V c =1.m/mn, Submergence deth=00mm) Seed (m/s) 1.800 1.575 1.50 1.15 0.900 0.675 0.450 0.5 0.000 Fgure 5. Flow attern at outorts of down 15 o angle wthout stes (left) and wth stes (rght) (V c =1.m/mn, Submergence deth=00mm) Incluson removal fracton to to (%) 0 5 0 15 10 5 0-15 -15ste 0 15 SEN outort angle ( o ) Fgure 5. 50μm ncluson removal to the to of the mold wth dfferent ort angle SEN (V c =1.m/mn, Submergence deth=00mm) FLUID FLOW AND INCLUSION MOTION IN MOLD REGION The velocty vector dstrbuton on the center face of the half strand s shown n Fgure 6, ndcatng a double roll flow attern. The uer loo reaches the menscus of the narrow face, and the second loo takes steel downwards nto the lqud core and eventually flows back towards the menscus n the strand center. The calculated weghted average turbulent energy and ts dssaton rate n the CC strand are 1.65 10 m /s and 4. 10 m /s resectvely. (a) Fgure 6. Flud flow n contnuous castng strands wth half deth, a: velocty near the SEN outort; b: velocty on the center face (00mm submergence deth, 1. m/mn castng seed, and no gas necton) The calculated tycal random traectores of bubbles and nclusons are show n Fgure 7. Smaller artcles enetrate and crculate more deely than the larger ones. (b) 4

ubbles larger than 1mm manly move n the uer roll. 0.mm bubbles can move wth aths as long as 6.65m and 71.5s before they escae from the to or become entraed through the bottom, whle 0.5mm bubbles move.4m and 1.6s, 1mm bubbles move 1.67m and 9.s, and 5mm bubbles move 0.59m 0.59s. (a) (b) (c) (d) (e) (f) (g) (h) Fgure 7. Flud flow n contnuous castng strands (00mm submergence deth, 1. m/mn castng seed, and no gas necton) (a: athlne, b: traectores of 50μm nclusons, c: traectores of 00μm nclusons, d: traectores of 0.mm bubbles, e: 1mm bubbles, f: flud flow seed (m/s), g: turbulent energy (m /s ), h: turbulent energy dssaton rate (m /s ) Comuted locatons of nclusons attached to the SEN walls and entraed at the wde faces of the slab are shown n Fgure 8. The calculaton suggests that around 4% nclusons leavng the tundsh stck to the SEN walls,.e., removal by cloggng. Fg.8 suggests roughly unform buldu on the nozzle walls, wth ncreased tendency towards buldu on the SEN bottom due to mact from the flowng et. Ths s consstent wth observatons of nozzle cloggng where local reoxdaton or chemcal nteracton were not the cause. The maorty of nclusons leavng the tundsh (more than 50%) are catured wthn 0mm of the surface, whch reresents the to.55m of the caster. Fg. 8 also shows that ncluson accumulaton eaks are at 1-14mm below the surface of the slab. A dsroortonately large fracton of these (15-16%) are catured n the narrow face, deste ts smaller surface area, owng to the et mngement aganst ts nner soldfcaton front. 5-8% nclusons extng the doman are entraed somewhere deeer n the nteror than 0mm shell thckness. A larger fracton of nclusons bgger than 50 µm are removed. For examle, 10% 5 μm nclusons leavng the tundsh are removed to the to of the mold by flud flow transort. The calculated ncluson removal from tundsh to slab by flud flow transort, summng u to SEN walls and the to surface of the mold, s 10-14%. Large nclusons (00μm) more tend to remove to the to, and small nclusons (50μm) recrculate more and most of them are flow out from the bottom. 5

INTERACTION ETWEEN INCLUSION AND ULE IN MOLTEN STEEL Fgure 10 shows the flud flow attern and traectores of 100µm nclusons around a 5mm bubble n molten steel. Inclusons tend to touch the bubble after the to ont. Stochastc fluctuaton of the turbulence makes the nclusons very dsersed, so attachment may occur at a range of ostons. Calculaton ndcates that the average turbulent energy n the doman has lttle effect on the fnal turbulent energy dstrbuton around the bubble. Fgure 8. Incluson locatons stckng to SEN walls (left) and to wde faces of the slab (rght) Incluson removal fracton to the to as functon of castng seed, ncluson sze and submergence deth s shown n Fgure 9. The removal fracton of <50μm nclusons s ndeendent of castng seed. Large nclusons are removed more wth decreasng castng seed, and large nclusons are more easly removed. It should be notced that nclusons as large as 00µm can only removed less than 75% due to the strong turbulence n the mold regon and small resdence tme of the molten steel n the molde regon. The calculated ncluson removal fracton as functon of submergence deth s a lttle surrsng because t ndcates that larger submergence deth removes a lttle more nclusons. Ths needs further nvestgaton to exlan. Incluson removal fracton to to (%) Incluson removal fracton to to (%) 75 70 65 60 55 50 45 40 5 0 5 0 15 75 70 65 60 55 50 45 40 5 0 5 0 15 10 50mm 00mm 00mm 0.8 1.0 1. 1.4 1.6 1.8.0 Castng seed (m/mn) (a) Submergence deth =150mm 00mm 00mm 50mm 50 100 150 00 50 00 Submergence deth (mm) (b) Castng seed =1.m/mn Fgure 9. Incluson removal fracton as functon of castng seed, ncluson sze, and submergence deth Fgure 10. Traectores of 100µm nclusons around a 5mm bubble n the molten steel (u: non-stochastc model, lower: stochastc model) The attachment robablty of nclusons (d P =5, 10, 0, 5, 50, 70,100μm) to bubbles (1,, 4, 6, 10mm) are calculated by the traectory calculaton of nclusons, whch ndcates that smaller bubbles and larger nclusons have larger attachment robabltes. 1mm bubbles can have ncluson attachment robablty as hgh as 0%, whle the ncluson attachment robablty to >5mm bubbles s less than 1%. To enable the comutaton of attachment rates for a contnuous sze dstrbuton of nclusons and bubbles, regresson s erformed on these calculated attachment robablty of nclusons (d P =5, 10, 0, 5, 50, 70,100μm) to bubbles (1,, 4, 6, 10mm), obtanng the followng equaton: P A = Ad (14) where A and deend on ncluson sze. In Eq.(11), P A s calculated by ths equaton. The corresondng ncluson removal fractons by bubble flotaton n the contnuous castng strand are shown n Fgure 11. Smaller bubbles aear to cause more ncluson removal wth the same gas flow rate. Secfcally, 1mm bubbles remove almost all of the nclusons larger than 0μm. However, t s unlkely that all of these small bubbles could escae from the to surface. Those that are entraed n the soldfyng shell would generate serous defects n the steel roduct. Increasng bubble sze above ~7mm roduces no change n removal rate, lkely due to the change n bubble shae offsettng the smaller number of bubbles. Thus, there should be an otmum bubble sze, whch gves not only hgh ncluson removal effcences, but also low entrament rates. The resent results suggest an otmal range of erhas -4mm. As shown n Fg.11, ncreasng gas flow rate causes more ncluson removal by bubble flotaton. The effect of turbulent Stochastc moton slghtly ncreases the ncluson removal by bubble flotaton. For the current CC condtons, ncludng a gas flow rate of 15 Nl/mn, the bubble sze s lkely to be around 5mm, assumng that there are a large number of 6

actve stes on the orous refractory that cause a gas flow rate of <0.5 ml/ore. 51) As shown n Fg. 11, about 10% total oxygen s removed by bubble flotaton. Ths corresonds to a m decrease n total oxygen. It has been redcted that 6-10% nclusons are removed to the to surface due to flow transort n the CC mold regon. Thus, the total redcted ncluson removal by flow transort and by bubble flotaton s around 16-0%. T.O. removal fracton by bubble flotaton (%) Removal fracton (%) 100 10 1 100 80 60 40 0 0 d =1mm d =mm d =mm d =4mm d =5mm d =10mm 0 0 40 60 80 100 10 140 Incluson dameter (μm) Sold curve: Stochastc Dash curve: Non-Stochastc Gas flow rate 15 Nl/mn 5 Nl/mn 1 Nl/mn 0.1 1 4 5 6 7 8 9 10 11 1 ubble dameter (mm) Fgure 11. Calculated ncluson removal by bubble flotaton (15 Nl/mn gas n left fgure) INDUSTRIAL TRIALS OF INCLUSION MEASUREMENTS The total oxygen n a Low Carbon Al-klled steel are measured, as shown n Table. Steady castng erod has a better cleanlness than unsteady castng erod (cast start, cast end and ladle change). And outer surface of the slab has large total oxygen than ts nsde. Inclusons extracted by Slmes test at the castng condton of 1.m/mn seed and 150mm SEN submergence deth were susended n water and ther sze dstrbutons measured wth a Coulter counter to get a -dmentonal ncluson sze dstrbuton. Ths obtaned the -dmensonal sze dstrbuton u to 6µm. The curves were extraolated to around 10µm as gven n Fgure 1 by matchng to the measured amount of extracted nclusons larger than 50µm. The nclusons mass fracton s 66.8m n the tundsh, 57.7m n the 0mm thckness nearest the slab surface, and averagng 51.9m n the slab. Ths suggests that nclusons n the nteror of the slab (.e., excet outer 0mm thckness of the slab) s 50.6m. The fracton of nclusons removed from tundsh to slab s around %. The numercal redcton and the measurement agree remarkably well, consderng that 4% nclusons are entraed to the SEN walls to cause cloggng. Frst cast sequence 1 4 Inner surface 0.004 0.0017 0.0015 0.0018 ¼ thckness 0.0046 0.0014 0.006 0.009 Center 0.004 0.0015 0.0018 0.00 ¾ thckness 0.001 0.001 0.004 0.00 Outer surface 0.004 0.001 0.0014 0.0018 mean 0.008 0.0016 0.0019 0.00 Second cast sequence 1 4 Inner surface 0.00 0.00 0.0018 0.0016 ¼ thckness 0.008 0.008 0.001 0.0019 Center 0.00 0.006 0.00 0.001 ¾ thckness 0.009 0.00 0.0016 0.0018 Outer surface 0.0045 0.00 0.0016 0.00 mean 0.004 0.00 0.0018 0.0019 1: Frst slab of frst heat; : Second slab of second heat; : Slab between and heats; 4: End of thrd heat Table. Slab total oxygen measurement (%) Incluson number densty (1/m steel) Inclusons (m) 10 11 10 9 10 7 10 5 10 10 1 10-1 10 - Inclusons n steel: Tundsh Slab (by flow transort and bubble flotaton) Inclusons n slab (only by bubble flotaton) ubble sze d =5mm ubble sze d =mm 0 0 40 60 80 100 10 140 Incluson dameter (μm) 7 6 5 4 1 (a) Tundsh Slab (surface 0mm) Slab (average) 0 Each dot s.14μm bn sze 0 0 40 60 80 100 10 140 Incluson dameter (μm) (b) Fgure 1. Incluson sze dstrbuton evoluton by Coulter Counter measurement of the Slme extracted nclusons The measured ncluson dstrbuton comared wth the redcton s shown n Fgure 1b. The ntal sze dstrbuton of nclusons n the smulaton s the sze dstrbuton n the tundsh. The redcted s the sze dstrbuton of nclusons after removed only by bubble flotaton. If consderng the ncluson removal by flow transort, the matchng between the calculaton and the measurement wll be much better. 7

CONCLUSIONS 1) Ths work resents a fundamental model of ncluson removal by flud flow transort and by bubble flotaton n the molten steel of a contnuous castng strand. ) Smaller bubbles and larger nclusons have larger attachment robabltes. ubbles smaller than 1mm dameter have ncluson attachment robabltes as hgh as 0%, whle the ncluson attachment robablty for bubbles larger than 5mm s less than 1%. The stochastc effect of turbulence (modeled by the random walk method) slghtly ncreases the attachment rate. ) In the CC strand, smaller bubbles enetrate and crculate more deely than larger ones. ubbles larger than 1mm manly move n the uer roll. 0.mm bubbles can move as far as 6.65m and take 71.5s before they ether escae from the to or are entraed through the bottom, whle 0.5mm bubbles move.4m and take 1.6s, 1mm bubbles move 1.67m and take 9.s, and 5mm bubbles move 0.59m and take 0.59s. 4) In the CC mold, f bubbles are ~ 5mm n dameter, ~10% of the nclusons are redcted to be removed by bubble flotaton, corresondng to around m decrease n total oxygen. Combned wth ~ 8% ncluson removal by flow transort and 4% by entrament to SEN walls as cloggng, the total roughly agrees well wth the measured ncluson removal rate by the CC mold of ~%. 5) Smaller bubbles are more effcent at ncluson removal by bubble flotaton, so long as they are not entraed n the soldfyng shell. 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