Inclusion Removal by Bubble Flotation in Continuous Casting Mold

Transcription

1 L. Zhang, J. Aok, & G Thomas, Materals Scence & Technology (MS&T), Se. 6-9,, New Orleans, LA. Incluson Removal by ubble Flotaton n Contnuous Castng Mol Lfeng Zhang, Jun Aok, ran G. Thomas Unversty of Illnos at Urbana-Chamagn, 6 W. Green St., Urbana, IL 68, USA Phone number: , Fax number: Emal: zhang@uuc.eu, Emal: bgthomas@uuc.eu Keywors: Incluson Removal, ubble Flotaton, Contnuous Castng Mol, Attachment Probablty Abstract Funamentally-base comutatonal moels are eveloe to quantfy the removal of nclusons by bubbles urng the contnuous castng of steel. Frst, the attachment robablty of nclusons on a bubble surface s nvestgate base on funamental flu flow smulatons, ncororatng the turbulent ncluson trajectory an slng tme of each nvual ncluson along the bubble surface as a functon of artcle an bubble sze. Then, the turbulent flu flow n a tycal contnuous castng mol, trajectores of bubbles an ther ath length n the mol are calculate. The change n ncluson strbuton ue to removal by bubble transort n the mol s calculate base on the comute attachment robablty of ncluson on each bubble an the comute ath length of the bubbles. In aton to quantfyng ncluson removal for many fferent cases, the results are mortant to estmate the sgnfcance of fferent ncluson removal mechansms. Ths work s art of a comrehensve effort to otmze steelmakng an castng oeratons to lower efects. Introucton The ever-ncreasng emans for hgh qualty have mae the steelmaker ncreasngly aware of rouct cleanlness requrements. Non-metallc nclusons can lea to excessve castng rears or rejecte castngs. Many methos have been eveloe to remove nclusons from molten steel. Gas njecton s commonly ale to many seconary metallurgcal rocesses such as lale treatment, the RH egassng vessel, an the Submerge Entry Nozzle (SEN) urng the contnuous castng (CC) rocess. Although t s well-known that gas njecton hels to remove nclusons, the mechansms an removal rates have not been quantfe. Ths work resents funamental moels to quantfy the removal of nclusons by bubbles n steel refnng rocesses an ales them to the contnuous castng mol for tycal contons. After revewng revous work on three relevant tocs, the moels an corresonng results are resente n three sectons: ) funamental ncluson - bubble nteractons, ) bubble trajectores an ) ncluson removal. Defects Relate to Inclusons an ubbles n Steel The eveloment of gas njecton rocesses focuses on achevng two contons: fne bubbles an goo mxng. Durng steel seconary refnng, fne bubbles rove large gas/lqu nterfacal area an hgh attachment robablty of nclusons to bubbles, an goo mxng enhances the effcency of the transfer of the alloy elements. ubbles njecte nto the SEN an CC mol have fve effects relate to steel qualty control: - Helng to reuce nozzle cloggng; - Helng to nfluence an control the flow attern n the mol; - Generatng to surface level fluctuatons an even emulsfcaton f the gas flow rate s too large; - Caturng nclusons movng wthn the molten steel, an removng them nto the to slag. [-] - Entrang nclusons nto the solfe shell, eventually leang to lne efects such as surface slvers, blsters, [,, -7] encl es or nternal efects n the rouct. Ae by surface tenson effects, sol nclusons agglomerate on surfaces such as bubbles, as shown n Fgure [8, 9]. Lne efects aear on the surface of fnshe str roucts, wth several tens of mcrometers to mllmeter wth an as long as.- meter []. Ths surface efect s beleve to result from nonmetallc nclusons caught near the surface of the slab (<mm from the surface). Ths efect s also calle slvers, or calle encl e f coule wth elongate bubbles. A serous encl e efect calle encl blsters on the fnshe rouct [] s a tubular shae surface efect, wth a smooth slghtly rase surface, tycally ~mm we an -mm long [, ] (Fgure [] ). The rocess of ncluson removal by gas bubbles s nfluence by many factors nclung the turbulent flu flow of the molten steel, the shae an sze of both the bubbles an the nclusons, surface tenson effects, an bubble removal rates,

2 whch are affecte by slag roertes. W.Pan et al stue the removal of artcles (~8µm n sze) by bubble flotaton n a water moel by analyzng hgh see camera hotos. [] Zhang an Tanguch stue ncluson removal by bubble flotaton n a water moel uner turbulent contons by measurng the artcle number ensty wth a Coulter Counter. [] Several aers stues the contrbuton of turbulence to the attachment of nclusons to bubbles n terms of turbulent energy ssaton rate n the water system. Schubert [] reorte that the attachment robablty P s relate to the bubble sze ( ), [ ] / artcle sze ( ), an turbulent energy ssaton rate (ε) by P ε ( C 7 ) ( 7 P + C ) uner the conton of ( ), whch can only be use, ν ε. For metallurgcal melts, the tycal value of the energy ssaton rateε s.-m /s, so ths equaton can be use only f, 8µm. Zhang et al [] erve the attachment robablty to be.6.. P ε Q, where Q g s the gas flow rate. Focusng on ncluson removal by bubble flotaton n lqu metal ( ) 6 g systems, Zhang scusse the funamentals of ncluson removal by bubble flotaton n the molten steel uner lamnar flow contons an tentatvely scusse the effect of turbulence; [] A.G.Szekely nvestgate the removal of sol artcles from the molten alumnum urng the snnng nozzle flotaton rocess; [] K.Okumura et al stue the removal rate of SO nclusons from the molten Cu to the slag uner gas njecton strrng contons; [6] Y.Mk et al nvestgate ncluson removal urng steel RH egassng conserng bubble flotaton as one of the ncluson removal methos [7]. Fg. Inclusons aroun bubble shae oman n the ngot steel (a,b,c) [8] an n the contnuous castng steel [9] Fg. Incluson slver n the longtunal secton of a sheet rouct [9], an tycal encl blster efect on a steel sheet []. ubble Sze n Molten Steel Gas can be njecte nto the molten steel by varous evces, such as tuyeres, lances, an orous refractory lugs. Large bubbles can breaku accorng to the local turbulence levels. The sze of the largest survvng bubbles can be estmate by the force balance mose on the bubble. [] The average equvalent sze of bubbles to survve n seconary steel refnng rocesses s -mm [, 8] an ~mm n the CC mol. ubble shae changes wth ts sze. Wellek et al [9] nvestgate the shae of bubbles n, an got the followng emrcal relatonsh,.77 e = +.6Eo, () where e s the asect rato of the bubble an Eo s the Eötvös number, whch reresents the rato between the buoyancy force an the surface tenson force by g ( ρ ρ g ) Eo =, () σ where g s the gravtatonal acceleraton, s bubble ameter, ρ an ρ g are enstes of the molten steel an the argon gas resectvely, an σ s the surface tenson of the molten steel. Fgure shows the asect rato e of bubbles n molten steel, ncatng that <mm bubbles are shercal, -mm bubbles are sheroal, an >mm bubble are shercal-ca shae. Most bubbles n steel refnng are shercal-ca shae. [-] The shae of the bubble also eens on the rato of the turbulent ressure fluctuaton to the callary ressure, whch s relate to the Weber number. If the bubble Weber number excees a crtcal value, the bubble wll breaku. Furthermore, t

3 has been shown that bubble sze s relate to the strrng ntensty of the lqu hase. [] Sevk an Park [] erve an exresson to etermne the maxmum bubble sze as a functon of strrng energy as Eq.(),. where σ max WeCrt. ( ) ε () ρ max s the maxmum bubble sze n m; ε s the turbulent energy ssaton rate n W/t; σ s the surface tenson n N/m ; ρ s the ensty of the molten steel n kg/m, an the crtcal Weber number We Crt.9-.. Eq.() ncates that hgher strrng ntensty favors smaller bubbles, as shown n Fgure. The strrng ntenstes of varous metallurgcal systems are also shown n ths fgure. [] The hghly turbulent flow n the SEN wll break u the gas nto fne bubbles aroun mm n ameter. The newly-eveloe swrl SEN [-7] may nuce larger energy ssaton rate by blang the flu flow wth hgh see, generatng much smaller bubbles. e = +.6 Eo.77 Shercal ca e Shere Shero a a e=a /a. (mm) Fg. ubble shae as a functon of ts sze ubble Termnal Velocty n Molten Steel The termnal velocty of bubbles rsng n molten steel s ffcult to measure accurately. Densty, vscosty an surface tenson of the lqu affect the bubble termnal velocty as o bubble sze an the turbulent flu flow characterstcs. Fgure shows the termnal veloctes of gas bubbles n the molten steel as calculate by fferent moels []. A smoothe mean of the bubble velocty recte by these moels s comare wth that of the current moel. max (mm) 6 We Crt =.9 We Crt =.. SEN outlet of contnuous castng mol. RH. VOD. ASEA-SKF. Tunsh nlet zone 6. t lales ε (W/tonne) U ( m/s ) - - J.R.Grace [] V.G.Levch [] F.N.Peebles [] R.M.Daves [] R.Clft [] 6 mean value of moel - 7 Current moel (zero shear) 8 Current moel (no sl) ( X - m) Fg. Maxmum Argon bubble sze versus bulk Fg. ubble termnal velocty n molten steel strrng ower

4 In ths work, the termnal velocty of a bubble can be calculate from a force balance between the buoyancy force (F ) an the rag force (F D ) actng on the bubble. The buoyancy force s exresse by π F = ρ ρ () 6 ( ) an the rag force F D s calculate usng FLUENT by ntegratng the surface force on the bubble. u j u FD ja = τ = δ j + µ + A () S S x x j where τ j s the shear force on the bubble surface, s the ressure, µ s the vscosty of the molten steel, u an u j are the velocty comonents of the flu flow, x an x j are the coornates, an δ j s the Kronecker elta, whch equals zero f =j, else equals unt. The rag force eens on the sze, velocty, an surface bounary conton of the bubble, whle the buoyancy force only eens on the bubble sze. y alyng F =F D, for a gven sze bubble an surface conton, the termnal velocty of the bubble can be obtane, also shown n Fg.. For a free bubble, the zero shear conton s more arorate than the no sl C. The alternatve surface bounary conton, no sl, s more arorate for bubbles wth rg surfaces, such as cause by surface-actve elements or coverng the surface wth artcles. Fg. shows that the calculate termnal velocty for free bubbles (zero shear surface conton) agrees well wth the mean of other moels. A eak occurs at a bubble ameter of mm exsts, where the bubble shae changes from shercal to ellsoal. Elsoal bubbles (- mm) have smlar velocty. For bubbles larger than mm, termnal velocty ncreases raly wth ncreasng sze ue to ther shercal ca shae. Incluson - ubble Interactons n Molten Steel Moel Formulaton The attachment rocess of an ncluson to a gas bubble n the molten steel rocees through the followng stes: the ncluson aroaches the gas bubble, an colles f t gets close enough. If the thn flm of lqu between the artcle an the bubble ecreases to less than a crtcal thckness, t wll suenly ruture causng the ncluson to attach ermanently to the surface of the bubble urng the collson. Otherwse, f t sles along the surface of the bubble for a long enough tme, the thn flm can ran away an ruture, agan leang to ncluson attachment. Otherwse, the ncluson wll move away an etach from the bubble. The collson tme, t c, starts wth the eformaton of the bubble by the ncluson an fnshes at the nstant of restoraton of the bubble to ts orgnal sze. The flm ranage tme, t F, s the tme requre for the ranage of the lqu flm between the bubble an the ncluson untl a crtcal flm thckness s reache an ruture occurs. The nteracton tme between the bubble an the ncluson, t I, nclues the tme whle the ncluson colles wth the bubble (collson tme) an ossbly sles across ts surface (slng tme). In ths work, t I s calculate from the ncluson centerlne trajectory results by trackng the tme that elases whle the stance from the ncluson center to the surface of the bubble s less than the ncluson raus. Then, f t I >t F, the ncluson wll be attache to the surface of the bubble. Ye an Mller [8] gve the collson tme as Eq.(6) C ρ = σ g t. (6) where ρ P s ncluson ensty (kg/m ). The collson tme eens manly on the ncluson sze, an s neenent of the bubble sze. H.J.Schulze [9] erve the ruture tme of the flm forme between a sol artcle an a gas bubble, t F α µ 6 kσ h Cr = (7) where k =. α s the angle (n ra) for the transton of the shercally eforme art of the bubble surface to the nonshercally eforme art, gven by Eq(8) [] P π ρu α = arccos. σ (8)

5 where Cr h s the crtcal thckness of lqu flm for flm ruture, gven by [] =. 8 [ σ ( cosθ )]. 6 h (9) Cr where θ s the contact angle of the nclusons. In orer to calculate the nteracton tme an the attachment robablty of nclusons to the bubble surface, a comutatonal smulaton of turbulent flow aroun an nvual bubble an a smulaton of ncluson transort through the flow fel are requre. Frst, the steay turbulent flu flow of molten steel aroun an argon bubble s calculate by solvng the contnuty equaton, Naver-Stokes equatons, an turbulent energy an ts ssaton rate equatons n two mensons, assumng axsymmetry. Possble eformaton of the bubble shae by the flow an ncluson moton s gnore. The nlet velocty an far-fel velocty conton are set to of the bubble termnal velocty, assumng a sutable turbulent energy an ssaton rate, an a far fel ressure outlet. The trajectory of each artcle s then calculate by ntegratng the followng artcle velocty equaton, whch consers the balance between rag an buoyancy forces. u t = ρ ρ C D ( u u ) ( ρ ρ ) where u,, s the artcle velocty, m/s; an C D, s the rag coeffcent gven below as a functon of artcle Reynols number (Re ), C D + Re (.86Re ) ρ P g () =. () To ncororate the stochastc effect of turbulent fluctuatons on the artcle moton, ths work uses the ranom walk moel n FLUENT. [] In ths moel, artcle velocty fluctuatons are base on a Gaussan-strbute ranom number, chosen accorng to the local turbulent knetc energy. The ranom number s change, thus roucng a new nstantaneous velocty fluctuaton, at a frequency equal to the characterstc lfetme of the ey. The nstantaneous flu velocty s gven by u u + u =, () u = ξ u = ξ k () where u s the nstantaneous flu velocty, m/s; u s the mean flu hase velocty, m/s; u s ranom velocty fluctuaton, m/s; ξ s the ranom number, an k s the local level of turbulent knetc energy n m /s. As bounary contons, nclusons reflect f they touch the surface of the bubble. Several thousan nclusons are unformly njecte nto the oman n the column wth ameter + for non-stochastc moel an far larger column than + for stochastc moel. The nclusons are njecte wth the local velocty at the lace of the - tmes of the bubble ameter far from the bubble center. If t s assume that there s no etachment after nclusons are attache to the surface of the bubble, the attachment robablty can be obtane by the followng stes. If the normal stance of the ncluson center to the surface of the bubble s frst less than the ncluson raus, the collson between the ncluson an the bubble takes lace. An f ths stance kees less than the ncluson raus for some tme, then t s the slng tme. Inclusons wll be attache to the surface of the bubble accorng to the crteron scusse before. The attachment robablty wthout conserng the stochastc effect can be efne as follows: N o o P = =, () N T + where N o s the number of nclusons attachng to the bubble by satsfyng ether t I >t F, an N T s the number of nclusons njecte nto the bubble column wth ameter + P. Wthout the stochastc effect, only artcles startng wthn a crtcal stance from the bubble axs os wll be entrae, as shown n Fgure 6a. If the stochastc effect s taken nto account, some nclusons nse the column of OS may not colle wth the bubble ue to ts ranom walk. On the other han other nclusons even far outse the column + may colle an attach onto the bubble surface. Thus, many nclusons must be njecte n a large column n orer to comute ths accurately. Then the attache robablty, as shown n Fgure 6b, can be obtane by

6 N = N ( π ( R + R) πr ) N N ( R R + R ) N N o, o, P A T, T, o, P = A + P π ( + ) ( + ) t, 8R R, () where N o s the number of nclusons attachng to the bubble by satsfyng ether t I >t F, A +P s the secton area of the column wth ameter of + P. N T s the total number of nclusons njecte through the area A, an s the sequence number of the annular oston at whch the nclusons are njecte. In the current nvestgaton, the followng arameters are use: ρ=7 kg/m, ρ P =8 kg/m, ρ g =.68kg/m, σ=. N/m, θ= o, µ=.67 kg/m-s, =-µm, an =-mm. These arameters reresent tycal shercal sol nclusons such as slca or alumna n molten steel. OS OC u P R R + R u bubble ubble b (a) Non-Stochastc (b) Stochastc Fg.6 Schematc of the attachment robablty of nclusons to the bubble surface. Results: Flu Flow an Incluson Moton Aroun a ubble Fgure 7 shows the flu flow attern behn a rg shere (.mm n ameter) n water. The smulaton agrees well wth the measurement. There s a recrculaton regon or swrl behn the sol artcle. Ths swrl s not observe n flu flow aroun a free bubble, as shown n Fgure 8. Fgure 8 shows the flu flow attern an trajectores of µm nclusons aroun a mm bubble n molten steel. The tracer artcles (7 kg/m ensty) follow the stream lnes an ten to touch the surface of the bubble at the to ont (exactly half-way aroun the bubble). Partcles wth ensty smaller than that of the lqu (such as nclusons n the molten steel) ten to touch the bubble after the to ont, whle enser artcles, such as sol artcles n water n mneral rocessng, ten to touch the bubble before the to ont. Stochastc fluctuaton of the turbulence makes the nclusons very serse, so attachment may occur at a range of ostons (Fg.8e) Fg.7 Smulaton (left) an exerment (rght [] ) of flu flow behn a rg shere (.mm n ameter) n water 6

7 (b) Incluson ensty: 8 kg/m (a) Stream Functon Fg.8 (c) Incluson ensty: 7 kg/m (). Incluson ensty: kg/m (e) Incluson ensty: 8 kg/m Flu flow an trajectores of µm nclusons aroun a mm bubble n the molten steel wth ensty of 7 kg/m (a-: non-stochastc moel, e: stochastc moel) The average turbulent energy n the oman has lttle effect on the fnal turbulent energy strbuton aroun the bubble. As shown n Fgure 9, Case a) has orers of magntue larger average turbulent energy than Case b), but has slght smaller local turbulent energy aroun the bubble. Ths s because Case b) has a hgher bubble termnal velocty than Case a). Fg.9 (a) (b) Turbulent energy strbuton aroun a mm bubble (a: average k.6 m/s,. m/s, an.9 m/s bubble termnal velocty; b: average k.6 8 m/s,.7 7m/s, an.6 m/s bubble termnal velocty) Durng the moton of bubbles n the molten steel, the flu flow attern aroun the bubble wll change as nclusons become attache, as shown n Fgurea. A recrculaton regon behn the bubble s generate even for only fve µm nclusons attache on the surface of the bubble. Ths recrculaton oes not exst behn a bubble that s free from attache nclusons. Thus, the flu flow attern aroun a bubble wth attache sol nclusons s more lke the sol artcles, such as shown n Fg. 7. Fgure b ncates that hgh turbulent energy locates aroun the nclusons attache on the bubble, an the turbulent energy n the wake of the bubble becomes smaller wth more nclusons attache. The k change aroun the bubble wll n turn affect the ncluson attachment to the bubble ue to the eenence of the ranom walk velocty fluctuaton on k (Eq.-). Wth the current attachment moel, ths henomena s not nclue, but wll be stue further..m/s.m/s No nclusons.m/s Fve µm nclusons attache (a) Flu flow attern... Ffty-three µm nclusons attache

8 wthout ncluson attachment Fg wth nclusons attache wth nclusons attache (b) Turbulent energy strbuton (k) Flu flow attern an turbulent energy strbuton aroun a mm bubble wth an wthout ncluson attachment Results: Incluson Attachment Probablty to ubbles tf, tc (µs) The calculate collson tme (Eq.(6)) an flm ranage tme (Eq.(7)) of nclusons uner ranom walk on a mm bubble are shown n Fgure. The collson tme an flm ranage tme both ncrease wth ncreasng ncluson sze, but the flm ranage ncreases more steely wth ncluson sze. The collson tme of nclusons smaller than µm, s larger than the flm ranage tme for >mm bubbles. The calculate normal stances from the center of µm nclusons to the surface of a mm bubble as functon of tme when nclusons aroach a mm bubble are shown n Fgure. Then the tme nterval when the stance s below the ncluson raus (µm) s the nteracton tme between the ncluson an the bubble, whch s also shown n Fg.. Larger nclusons have greater nteracton tme, on the orer of ml secon. If nclusons sle on the surface of the bubble, aroun 99.7% µm nclusons, aroun 99.% µm nclusons, an aroun 9.% µm nclusons wll be attache on the surface of the bubble. tf =mm =mm =mm tc (µm) Fg. The collson tme an flm ranage tme of nclusons aroun a mm bubble The attachment robablty of nclusons (P=,,,,, 7,µm) to bubbles (,,, 6, mm) are calculate by the trajectory calculaton of nclusons wthout conserng the stochastc effect, as shown n Fgure, whch ncates that smaller bubbles an larger nclusons have larger attachment robabltes. mm bubbles can have ncluson attachment robablty as hgh as %, whle the ncluson attachment robablty to >mm bubbles s less than %. To enable comutaton of attachment rates for a contnuous sze strbuton of nclusons an bubbles, regresson was erforme on these calculate attachment robablty of nclusons (P=,,,,, 7,µm) to bubbles (,,, 6, mm). The results are shown n Table I. The regresson equaton obtane, Eq.(6), s nclue n Fg.. P = A (6) 8

9 where A an are = (7) A + where s n mm, s n µm.. =.77 (8). mm bubble. P = µm Interacton tme (s).. µm =µm µm µm µm Dstance from the bubble axs (mm) Fg. The normal stance from the center of µm nclusons to the surface of a mm bubble (left), an the nteracton tme of nclusons on a mm bubble (rght) The examle attachment robabltes of nclusons to a bubble nclung the stochastc effect of the turbulent flow are shown n Table II. The Stochastc effect slghtly ncreases the attachment of nclusons to the bubble surface. Fgure shows that by nclung the stochastc effect, µm nclusons n the column wth mm n ameter have oortuntes to collson an attach to the mm bubble surface, an the largest attachment oortunty s at the borer of mm ameter. Whle, wthout conserng the stochastc effect, only an all of the µm nclusons n the column wth.7mm n ameter attach to the bubbles. Owng to the extra comutatonal effort requre for the stochastc moel, t was not erforme for all szes of bubbles an nclusons. The Stochastc attachment robablty was estmate from the cases to be 6./.6=. tmes of the non-stochastc attachment robablty. Attachment Probablty (%). ubble ameter (mm) 6 g Dots: Numercal smulaton (NS) small ots an lnes: Regresson from NS Incluson ameter (µm) Table I. Regresse ncluson attachment robablty to the bubble larger than mm. Fg. The calculate an regresse attachment robablty of nclusons to bubbles 9

10 Table II Attachment robabltes of nclusons wth an wthout ranom walk to a mm bubble Case Case Average turbulent energy (m /s ) Average turbulent energy ssaton rate (m /s )..7 7 ubble velocty (m/s).9.6 ubble ameter (mm) Inclusons ameter (µm) Attachment Non-Stochastc moel robablty(%) Stochastc moel 6. / 9. Number of nclusons attache on mm bubble er 6 nclusons ubble ameter: mm k=. W/tone steel Attachment robablty (%).... ubble ameter: mm k=. W/tone steel Total Probablty: 6.% Fg Dstance from the axs (mm) Dstance from the axs (mm) Attachment robablty of µm nclusons to a mm bubble nclung the effect of ranom walk Moel Formulaton Flu Flow an ubble Moton n the Contnuous Castng Stran The three mensonal sngle hase steay turbulent flu flow n the SEN an CC stran s calculate by solvng the contnuty equaton, Naver-Stokes equatons, an turbulent energy an ts ssaton rate equatons. [, ] The trajectores of bubbles are calculate by Eq.(), nclung the effect of chaotc turbulent moton usng the ranom walk metho. ubbles escae at the to surface an the oen bottom, are reflecte at other faces. If the bubbles escae from the bottom, then s consere to be entrae by the solfyng shell. Ths s very crue relmnary aroxmaton of bubble removal, whch s beng nvestgate further as art of ths roject. The entrament of artcles to the solfyng shell s very comlex an s recevng well-eserve attenton n recent work. [-6] The SEN s wth 8mm bore sze, an own o outort angle, an 6 8mm outort sze. The submergence eth of the SEN s mm, an the castng see s. m/mn. Half wth of the mol s smulate n the current stuy (.m length m half wth.m thckness). The calculate weghte average turbulent energy an ts ssaton rate at the SEN outort are. m /s an.7 m /s resectvely. Accorng to Fg., the maxmum bubble sze s aroun mm. The velocty vector strbuton on the center face of the half stran s shown n Fgure, ncatng a ouble roll flow attern. The uer loo reaches the menscus of the narrow face, an the secon loo takes steel ownwars nto the lqu core an eventually flows back towars the menscus n the stran center. The calculate weghte average turbulent energy an ts ssaton rate n the CC stran s.6 m /s an. m /s resectvely. ubble Trajectory Results The calculate tycal ranom trajectores of bubbles are show n Fgure 6. Smaller bubbles enetrate an crculate more eely than the larger ones. ubbles larger than mm manly move n the uer roll..mm bubbles can move wth aths as long as 6.6m an 7.s before they escae from the to or become entrae through the bottom, whle.mm bubbles move.m an.6s, mm bubbles move.67m an 9.s, an mm bubbles move.9m.9s. The mean of the ath length (L ) an the resence tme (t ) of the bubbles are shown n Fgure 7, an the followng regresson equatons are obtane: 9.68ex = L (9)

11 . = ex.6ex +.9 ex t () where the ath length L an bubble sze are n m, an the resence tme t s n s. Wth the ath length an the resence tme, the bubble aarent moton see s obtane by W =L /t. The followng regresson equaton s obtane: W.7( ). 87 = () Larger bubbles have larger aarent moton see, whch can be as hgh as. m/s for mm bubbles See (m/s) Half Mol Wth (m).. (m) Fg. Flow attern n the CC stran center face wth half wth (velocty vectors, streamlne, turbulent energy k m /s an ts ssaton rate ε m /s resectvely) (a).mm (b).mm (c) mm () mm Fg.6 Tycal bubble trajectores n the mol wth half wth

12 Fg.7 Path length of bubbles (m) 7 6 Path length Aarent bubble moton see Resence tme ubble ameter (mm) The mean ath lengths, resence tmes an aarent see of bubbles n the CC stran Resence tme of bubbles (s)..... Aarent bubble moton see (m/s) Moel Formulaton Incluson Removal by ubbles n the CC Stran A removal moel of nclusons from the molten steel by bubble flotaton s eveloe for the molten steel-slca nclusonsargon bubbles system. The followng assumtons are use: - ubbles all have the same sze; - Inclusons have a sze strbuton an are unformly strbute n the molten steel, an they are too small to affect bubble moton or the flow attern; - Only the nclusons remove by bubble flotaton are consere. The transort an collson of nclusons are gnore. - The bubble sze an the gas flow rate are chosen neenently; - Once stable attachment occurs between a bubble an an ncluson, there s no etachment an the ncluson s consere to be remove from the molten steel, owng to the hgh removal fracton of most bubbles. If a bubble wth ameter of s njecte nto the molten steel, the number of nclusons wth ameter whch attach to ths bubble, N A, urng ts moton s P N A, = π L n, () where L s the ath length of the bubble (m), gven by Eq.(9), an P s the attachment robablty of the ncluson to the bubble (%), gven by Eq.(6), an n s the number ensty of that ncluson sze. The volume of molten steel oure nto the stran (m ) n tme t (s) s V V C M = S t () 6 where castng see V C s n m/mn, S s the area of the slab secton (=..m ), The number ensty of nclusons (/m steel) remove by attachment to ths bubble s n A N V A,, = () Assumng that all nclusons are Al O, the oxygen remove by ths bubble (n m) then can be exresse by M

13 O = whch can be rewrtten as n A π P L n, π ρ 8 6 π ρ 8,, =, 6 ρ M VC S t 6 ρm 6 O =.6 V C L S t ρ ρ M ( n P ) ecause t s assume that all bubbles n the molten steel have the same sze, the total number of bubbles wth ameter enterng the molten steel urng tme t s whch can be rewrtten as n n = TM QG 7 t π 6 QGT 7π M t,, 6 () = (6) where Q G s the gas flow n Nl/mn, T M s the steel temerature (8K), an the factor of ½ s ue to the smulaton oman of a half mol. Therefore the total oxygen removal can be exresse by n = L ρ O.6 V S t ρ j= C M ( n, PA,, ) where n, s the number ensty of ncluson wth ameter, when bubble j s njecte, whch can be reresente by j n, j = n, j ( P ) π L VC S t 6 Ths equaton uates the ncluson number ensty strbuton after the calculaton of each nvual bubble, n orer to account for the sgnfcant change n ncluson concentraton cause by the smultaneous ncluson removal of many bubbles. j (7) (8) Results an Dscusson The ncluson sze strbutons measure n the tunsh above the outlets an n the CC slab are shown n Fgure 8 together wth the calculate sze strbutons after ncluson removal by bubble flotaton for several fferent bubble szes. The corresonng ncluson removal fractons are shown n the ajacent frame. If the bubbles were larger than mm, less than % of the nclusons can be remove by bubble flotaton at the gas flow rate of Nl/mn. Ths corresons to a m ecrease n total oxygen, as shown n Fgure 9. Smaller bubbles aear to cause more ncluson removal for the same gas flow rate. Secfcally, mm bubbles remove almost all of the nclusons larger than µm. However, t s unlkely that all of the bubbles that are ths small coul escae from the to surface. Those that are entrae n the solfyng shell woul generate serous efects n the steel rouct, such as shown n Fg.-. Increasng bubble sze above ~7mm rouces no change n removal rate, lkely ue to the change n bubble shae offsettng the smaller number of bubbles. As shown n Fgure 9, ncreasng gas flow rate causes more ncluson removal by bubble flotaton. Conserng the effect of turbulent Stochastc moton slghtly ncreases the ncluson removal by bubble flotaton. For the current CC contons, nclung a gas flow rate of Nl/mn, the bubble sze s lkely to be aroun mm, assumng there are a large number of actve stes on the orous refractory that cause a gas flow rate of <. ml/ore. [7] As shown n Fg. 9, about % total

14 oxygen s remove by bubble flotaton. Prevous nvestgatons ncate that ~8% of the nclusons are remove to the to surface ue to flow transort n the CC mol regon. [8] Thus, the total recte ncluson removal by flow transort an by bubble flotaton s aroun 8%. The measure ncluson mass fracton s 66.8m n the tunsh, an averages.9m n the slab, whch corresons to % removal n the mol (Fg.8). The recton an the measurement agree remarkably well, conserng that some nclusons are lkely entrae to the SEN walls to cause cloggng. Incluson number ensty (/m steel) Tunsh measurement Slab measurement Precton, =mm Precton, =mm Precton, =mm Removal fracton (%) 8 6 =mm =mm =mm =mm =mm =mm Incluson ameter (µm) Incluson ameter (µm) Fg. 8 Measure an calculate ncluson sze strbuton wth fferent sze bubble flotaton ( Nl/mn gas) T.O. removal fracton by bubble flotaton (%) Sol curve: Stochastc Dash curve: Non-Stochastc Gas flow rate Nl/mn Nl/mn Nl/mn ubble ameter (mm) Fg. 9 Calculate ncluson removal by bubble flotaton Decreasng bubble sze s shown n Fgs. 8 an 9 to be more effcent at removng nclusons. As scusse before, however, small bubbles, such as those < mm, may be trae nto solfyng shell whle movng through the lower recrculaton zone. Thus, there shoul 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 -mm. Due to caturng many nclusons on ts surface, the aarent ensty of the bubble wth attache nclusons ncreases. Accorng to the current flu flow an nclusons conton n the CC mol, the calculate aarent ensty of the bubble ecreases wth ncreasng bubble sze (Fgurea). The maxmum aarent bubble ensty s only aroun.kg/m. Although ths s much greater than the orgnal argon gas ensty of.68 kg/m, t s stll far smaller than that of the molten steel, so has lttle effect on the bubble moton or bubble resence tme n the stran (Eq.()). The nclusons attache to each bubble also have a sze strbuton as shown n Fg.b. There are tycally several thousan nclusons recte to be attache to the bubble surface, whch matches well wth the measurements n Fg.c. Larger bubbles cature more nclusons than smaller ones (Fg.b) er bubble. Ths s nsuffcent to make u for ther smaller number, an furthermore makes them more angerous f cature, so large bubbles shoul be avoe.

15 Densty of bubble wth attache nclusons (kg/m ) Gas flow rate: Nl/mn Stochastc moel. 6 8 ubble ameter (mm) Number of nclusons attache on a bubble ubble sze mm mm mm mm Incluson ameter (µm) Fg. The calculate aarent ensty of bubbles wth attache nclusons (a) an the calculate (b) an measure (c [] ) number of nclusons attache on the bubble n the steel Summary Ths work resents a funamental moel of ncluson removal ue to bubble flotaton n molten steel rocessng. The moel s valate wth avalable measurements an ale to rect the changes n ncluson strbuton that occur n the mol regon of a contnuous slab caster. Secfc moel fnngs nclue: ) In molten steel, bubbles smaller than mm ten to shercal, -mm bubbles are sheroal, an bubbles larger than mm are shercal ca shae. The bubble sze eens manly on the gas flow rate, njecton metho an strrng ower n the molten steel. The average equvalent sze of bubbles s estmate to be ~mm n the CC mol nvestgate n ths work. ) Inclusons ten to frst touch the bottom se of the bubble (ast the to ont), although stochastc fluctuatons ue to turbulence causes many varatons. The flu flow attern aroun a bubble wth attache sol nclusons s smlar to that of flow aroun a large sol artcle. Inclusons attache to the bubble surface also affect the strbuton of turbulent knetc energy aroun the bubble. ) The tme requre for flm ruture an attachment ncreases wth ncreasng nclusons sze. Surface tenson effects requre relatvely small slng tmes for alumna an slca n molten steel, whch mroves artcle removal. Secfcally, the requre slng tmes lower the ncluson attachment rates by only.% ( µm nclusons) to.7% ( µm nclusons). ) Smaller bubbles an larger nclusons have larger attachment robabltes. ubbles smaller than mm ameter have ncluson attachment robabltes as hgh as %, whle the ncluson attachment robablty for bubbles larger than mm s less than %. The stochastc effect of turbulence (moele by the ranom walk metho) slghtly ncreases the attachment rate. ) In the CC stran, smaller bubbles enetrate an crculate more eely than larger ones. ubbles larger than mm manly move n the uer roll..mm bubbles can move as far as 6.6m an take 7.s before they ether escae from the to or are entrae through the bottom, whle.mm bubbles move.m an take.6s, mm bubbles move.67m an take 9.s, an mm bubbles move.9m an take.9s. 6) In the CC mol, f bubbles are ~ mm n ameter, ~% of the nclusons are recte to be remove by bubble flotaton, corresonng to aroun m ecrease n total oxygen. Combne wth ~ 8% ncluson removal by flow transort, the total roughly agrees wth the measure ncluson removal rate by the CC mol of ~%. 7) Smaller bubbles are more effcent at ncluson removal by bubble flotaton, so long as they are not entrae n the solfyng shell. Larger gas flow rate favors ncluson removal by bubble flotaton. The otmum bubble sze shoul be -mm. 8) Attache nclusons ncreases the bubble ensty several tmes, but oes not affect ts moton because the aarent ensty s stll far smaller than that of molten steel. 9) Future research wll focus on: - The stochastc robablty of all ncluson an bubble szes, - The effect of bubble sze strbuton on the removal of nclusons, - Coulng wth a moel of multhase flu flow n the CC mol,

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