COUPLED HEAT AND MASS TRANSFER APPROACH TO SIMULATE THE SCRAP DISSOLUTION IN STEELMAKING PROCESS

Transcription

1 Inernainal Sympsium fr Research Schlars n Meallurgy, Maerials Science & Engineering Decemer 18-, 6, Chennai, India Organised y Dep. f Meallurgical & Maerials Engineering, IIT Madras, Chennai, India ISSN X COUPLED HEAT AND MASS TRANSFER APPROACH TO SIMULATE THE SCRAP DISSOLUTION IN STEELMAKING PROCESS Ajay Kumar Shukla 1,Prf Brahma De 1 1 Deparmen f Maerials and Meallurgical Engineering, Indian Insiue f Technlgy Kanpur, 816, India {shukla@,de@}iik.ac.in Keywrds : scrap dissluin, seelmaking, xygen seelmaking, mahemaical mdel, mving undary, analyical sluin ABSTRACT Scrap is used as ne f he asic irn earing charge maerials in seelmaking prcesses, in addiin h meal. The kineics f dissluin f scarp can e a limiing facr in he cnrl f he emperaure rajecry f a seelmaking prcess. I is als knwn affec he slag frmain, slag faming and he ps cmusin rai in he iniial sages f he lw. The mechanism f scrap dissluin cmprises f simulaneus hea ransfer and mass ransfer (f carn) in he ulk meal and in he scrap. A prper undersanding and accurae predicin f he scrap dissluin rae is a key facr design a suiale dynamic cnrl sraegy fr a seelmaking prcess. In he presen wrk, h analyical and numerical mdels have een develped predic he dissluin ehavir f scrap in an xygen seelmaking cnverer. The effec f varius shapes (nly cylindrical) and sizes f scrap, he carn cmpsiin f meal, emperaure and he carn cmpsiin rajecry in he ulk under frced cnvecin cndiins f hea and mass ransfer are incrpraed in he mdel. Fr he firs ime, a cmparisn is made eween he analyical and numerical sluins fr he case f a cmplex mving undary prlem. The resuls f he calculain ained frm h he mdels have een criically analyzed and he impran parameers are evaluaed. The mdels can e direcly used predic he limiing size and als he pimal rai f liquid meal scrap in a seelmaking prcess. INTRODUCTION Scrap is added as raw maerial which cmpensaes fr he excess hea generaed due varius chemical reacins in seelmaking prcess. The prcess is cming under he special caegry f slidificain and meling prlems called as mving undary prlems wih phase change (Sefan prlems). Depending upn he hea efficiency f he prcess i is pssile cnsume scrap y 3% in xygen seelmaking prcess.

2 Several sudies have een carried u invesigae he prcess f scrap dissluin in seelmaking cnverers. Ms f he mdels have een develped fr hea ransfer in a single direcin where hea and mass ransfer cefficiens eween slid and liquid mel were esimaed y semi-empirical crrelains under he cndiins f naural and frced cnvecin. Since here is l f urulence in he ah due rigrus chemical reacins such as decarurizain and m sirring s effr has een made crrelae he hea ransfer cefficien as a funcin f al energy inpu he sysem. There exiss relainship eween hea and mass ransfer cefficiens under frced cnvecin cndiin knwn as Chiln-Clurn analgy. Since during dissluin f scrap undary layer a slid liquid inerface is als mving s he acual values f hea and mass ransfer cefficiens are differen frm he ulk values. Hea and mass ransfer equains ained in his way are cupled geher esimae he dissluin ehavir f cylindrical shape scrap fr varius sizes under differen cndiins like rajecry f Temperaure and Carn cmpsiin in he ulk, paren scrap cmpsiin, perain parameers f he prcess (lwing regime and decarurizain prfile) ec. The esimaed values f dissluin ehavir and al ime fr dissluin is cming in clse agreemen wih he servains. THEORETICAL CONSIDERATIONS Slidificain and meling prcess is gverened y hea and mass ransfer eween liquid and slid phases. The hea and mass ransfer equains are cupled geher arrive a he desired sluin. Le us cnsider he inerface eween liquid and slid seel during dissluin prcess. Figure 1 Schemaic diagram f emperaure and cmpsiin prfile in scrap and meal Figure 1 shws he emperaure and carn cmpsiin prfile fr meling f slid scrap in liquid mel. The ulk has a emperaure f T and carn cmpsiin f C. The slid scrap has he unifrm emperaure and carn cmpsiin f Ts and Cscrap respecively. The emperaure and cmpsiin f slid-liquid inerface are Ti and Ci respecively. There exiss hermdynamic equilirium eween slid and liquid carn cmpsiin a he inerface frm which he cmpsiin f scrap in slid a he inerface is esimaed as Cs.The fllwing mahemaical equains have een used descrie he dissluin ehavir f scrap in he liquid mel (calculains dne fr hea and mass ransfer in ne dimensin ) : dt Hv h( T Ti) [E1] dx x

3 T ( x, ) x T ( x, sc sc ) v(ci-cs)=k(ci-c) [E] [E3] =mass densiy f he scrap =hermal diffusiviy f slid scrap h=hea ransfer cefficien eween liquid and slid k=mass ransfer cefficien eween liquid and slid v=he mving velciy f he inerface (slidificain/meling rae ) H=he laen hea f meling hermal cnduciviy in he slid seel. Equain [E1] represens hea alance a he inerface, and equain [E] represens he hea cnducin in he slid scrap and equain [E3] descries mass alance f carn a he inerface.the esimaed velciy f inerface may e psiive(slidificain) r negaive(meling) depending upn he dminance f he hea ransfer y cnducin inside he scrap.therefre verall dissluin prcess is defined as simulaneus hea and mass ransfer (f carn) in he mel and inside he scrap. Iniial mel is geing slidified n cld paren scrap fllwed y remeling f he slidified shell and meling f he paren scrap. DESCRIPTION OF THE MATHEMATICAL MODEL Equain [E1] and [E] has een slved y analyical mehd alng wih suiale iniial and undary cndiins aining sluin as a Furier series in ur previus wrk 1.In rder sudy he scrap dissluin prcess in a cmplee way, hea and mass ransfer equains have een cupled geher where hea ransfer cefficien in ulk has een esimaed as a funcin f al inpu energy he xygen seelmaking prcess and mass ransfer cefficien y chiln-clurn analgy fr he frced cnvecin siuain. Furher mahemaical reamen is given esimae he hea and mass ransfer cefficiens fr he mving undary siuain. The velciies esimaed y hea and mass ransfer equains are cmpared fr differen values f inerface carn ill hey are cnverged give he crrec sluin. Fllwing se f assumpins are made fr frmulaing he mdel : 1. Thermal cnduciviy,densiy are same fr scrap as well as liquid mel.. Acual values f hea and mass ransfer cefficiens are calculaed frm mving undary layer cncep. 3. The slid scrap a he inerface is carurized and is in equilirium wih he liquid a he inerface. This is sujec he cndiin ha he esimaed equilirium cmpsiin in he slid scrap a he inerface cann e lesser han he paren cmpsiin. I is defined in he fllwing way : If Cs esimaed in he fllwing way is greaer han Cscrap hen Cs (1 C )exp v k Oherwise Cs = Cscrap (1)

4 4. The cmpsiin f he slidified shell in early sage f slidificain is calculaed frm he equain : Velciy ln( Ci Cs / C Cs ) () Where Ci and Cs are in hermdynamic equilirium wih each her. 5. Liquidus Line f Fe-C sysem is defined fr he inerface Temperaure and Carn cmpsiin as fllwing : Ti Ci 6. Velciy f he mving inerface is cnsan fr small ime sep. 7. The laen hea f slidificain des n include he addiinal erm accun fr he energy required raise he emperaure f meling mass frm inerface emperaure he ulk emperaure.this effec is aken care in equain (5),while defining he acual hea ransfer cefficien. (3) 8. The scrap is assumed e unifrmly expsed all he surfaces. Mahemaical Frmulain : 1.Hea Transfer Cefficien : Fr mving undary layer,hickness f he hermal undary is given as : k / h Acual value f hea ransfer cefficien is given as : (4) h m Cpm Velciy /( 1 Exp( m Cpm Velciy / h)) (5). Mass Transfer Cefficien : The hickness f he cncenrain undary layer is given as : m Dc / (6) Acual value f mass ransfer cefficien is given as : Velciy /( 1 Exp( Velciy / ) (7) 3.Hea flux alance a he slid-liquid inerface : h ( Rl)( T Ti) ( Rl) Hfe Velciy k ( Rl) ( dt / dr) r R (8a1)

5 where : dt dr r R i i 1 ( Tsci T '( R, ' ) Exp R i R (8a) Hf e Hfe ; During slidificain (8) Hfe ' Hfe Cp( T Tav) ; During fas and nrmal meling (8c) where average Temperaure f he meling shell is given as Tav R velciy Tsc( r, ) r dr R (8d1) R( R Velciy ) 4. Mass flux a inerface : Velciy( Cs Ci) ( Ci C ) (9) 5. Change in he hea cnen f he mel : Slidificain : CpWm( dt / d) h( Rl)( T T Fas and Nrmal meling : ) (1) CpWm( dt / d) h( Rl)( T T ) Cpm( T Tav)( dwsc / d) (11) where : ( dwsc / d) ( Rl) Velciy 6. Change in Carn cnen f he mel : Slidificain : Wm( dc / d) ( C rci)( Rl) Velciy (1) Fas and Nrmal Meling Wm( dc / d) ( C Cs)( Rl) Velciy (13) 7. Assumed Carn and Temperaure rajecry fr he case when scrap is n charged :

6 1.4 C Ciniial.17 if 3 Ciniial. 38 if Exp (.479 ) if C.5 (14) T Tiniial (15) where is he ime in minues. 8. Temperaure prfile esimain inside he scrap : i ( Tsci T '( R, ')) i i Tsc( r, ) T '( R, ') J ( r) Exp (16a) i. J ( i) R R i Relainship eween hea and mass ransfer cefficien : Hea and mass ransfer cefficiens fr fixed undary siuain may e relaed y Chiln- Clurn similariy as fllwing : Dc Calculain Prcedure :.6667 m h Cpm (17) 1. Prcess is divided in a numer f ime seps..temperaure prfile is calculaed inside he scrap a every ime sep 3. Hea and Carn mass ransfer equains are cupled geher in he fllwing way depending upn he he rai eween he cnducive and cnvecive hea flux a he inerface : If Cnducive _ Hea _ Flux _ a _ Inerface Cnvecive _ Hea _ Flux _ a _ Inerface >.1 Velciy f he mving inerface is calculaed as fllwing : 1 dt Velciy h'( T T ') k r R ( Hfe') dr (18) ( Cs C ) Velciy ln (19) ( Cs Ci) Where (19) is cming afer plugging in value f in equain (9). Equain (18),(19)alng wih (3) are slved simulaneusly y ierain mehd fr hree unknwns namely Velciy,Ti and Ci.

7 Cnducive _ Hea _ Flux _ a _ Inerface If <.1 Cnvecive _ Hea _ Flux _ a _ Inerface Then (dt/dr) r=r may e negleced and y cmining equain (18) and (5) we have fllwing equain : Velciy = m Cpm Cpm m ( T T ') ln 1 () m Hfe Afer cupling his equain wih equain (19) and y Chiln-Clurn analgy fr relainship eween hea and mass ransfer cefficien,we have :.6667 ( Cs C ) Cpm m ( T T ') ln = ln 1 (1) ( Cs Ci) Dc m Hfe Equain (1) alng wih (3) may e slved fr w unknwns Ti and Ci and frm hem Velciy may e calculaed using equain (). 5. C and T are updaed a each ime sep as explained frm equain (1) (15). 6. Wm and Wscr are updaed a each ime sep as fllwing : Wm( ) Wm( ) ( Rl) Velciy () Wscr( ) Wscr( ) ( Rl) Velciy Prcess Cndiins fr which simulain has een dne : W f liquid mel = 13 Kg Scrap Rai =.1 Iniial Temperaure = 1573 K Mel Carn Cmpsiin = 4.5 % Scrap Carn Cmpsiin =.5 % h_frac =.5 Lance Angle = 14 degrees Numer f penings in lance = 6 Thra Diameer =.46 cm Bah Deph = 1.3 m Lance Oxygen Flw Rae = 4 NM3/Min Bm Sirring Flw Rae = Nm3/min Blwing Regime is defined as fllwing : If < < 135 ; Lance heigh =. m If 135< <5 ; Lance heigh =. m If 5 < < 3 ; Lance Heigh = 1.8 m If > 3 ; Lance Heigh = 16 cm Mass ransfer vs hea ransfer cnrl RESULTS AND DISCUSSIONS

8 Based upn he calculaed resuls, fllwing differen znes f cnrl f prcess wih respec hea and mass ransfer have een ulined : If ( T Tl ) and ( C Cs ), The Prcess is cnrlled y hea and mass ransfer h fr smaller differences f T and T l. Fr larger differences hea ransfer is he nly cnrlling mechanism. If ( T Tl ) and ( C Cs ),The Prcess is cnrlled nly y he hea ransfer. If ( T Tl ) and ( C Cs ), The Prcess is cnrlled nly y he mass ransfer. If ( T Tl ) and ( C C s ), Dissluin des n ake place, As i is verified frm figure ha rae f dissluin is slw and mass ransfer cnrlled as lng as he emperaure f he mel is elw he liquidus emperaure f he scrap. When emperaure f he mel is greaer han he liquidus emperaure f he scrap, rae f dissluin increases very fas as i is hea ransfer cnrlled. Ave findings give an impressin ha he lwing sraegy mus e develped in such a manner ha decarurizain rae in early mmen shuld n e fas enugh reduce he carn level f he mel significanly. s Dimensin and Bulk Temperaure (a reduced scale ) f cylindrical shape scrap (Hea Transfer Cefficien calculaed as a funcin f Radius (Iniial Diameer = 1 cm) Radius (Iniial Diameer = cm) Radius (Iniial Diameer = 3 cm) Radius (Iniial Diameer = 4 cm) Bulk Temperaure (Iniial Diameer = 1 cm) Bulk Temperaure (Iniial Diameer = cm) Bulk Temperaure (Iniial Diameer = 3 cm) Bulk Temperaure (Iniial Diameer = 4 cm) Meling Temperaure f he Scrap Time (in Secnds ) Figure - : Dissluin ehavir f cylinder wr ulk emperaure Hea ransfer cefficien vs dissluin ehaviur In figure 3-4 dissluin ehavir is pled fr he hea ransfer cefficien value given in lieraure (475 W/M K) and fr he value calculaed as a funcin f lwing cndiins fr cylindrical gemeries. The al ime fr dissluin is cming is cming in eween 5

9 1 minues which is in clse agreemen wih he indusrial servains. The resuls are alms same fr h he cases which prves ha average hea ransfer cefficien as given in lieraure is in clse agreemen wih wha has een calculaed y he cnsiderain f average energy inpu he sysem.tal ime fr dissluin is decreasing n increasing he hea ransfer cefficien and als n prprinal he iniial size f he scrap which is cnrary he previus findings 8. Figure-3 : Dissluin ehavir f cylindrical shape scrap

10 Tal Time fr Dissluin vs Size (fr Cylindrical shape scrap ) 7 65 Hea Transfer Cefficien = 5 W/MK Hea Transfer Cefficien = 475 W/MK Hea Transfer Cefficien calculaed as a funcin f lwing cndiins Iniial Radius (in M ) Figure 4 : Tal ime fr cmplee dissluin vs dimensin CONCLUSION Mahemaical mdel fr dissluin f scrap in high carn mel is develped y cupled hea and mass ransfer apprach where emperaure prfile in he scrap is descried as pwer series ased sluin 1.and he hea ransfer cefficien is esimaed as a funcin f energy inpu he sysem. The resuls prve ha i is a gd apprximain assume he value f hea ransfer cefficien as 475 W/M /K which is in agreemen wih he calculains f D Herg and Sneijer. Furher wrk is ging n esimae he cmplee analyical sluin y Green s funcin apprach fr he same. I is als a maer f invesigain find u he level f cnac eween slidified shell and he paren scrap y perfrming experimens hwever requisie mdificain in hea ransfer cefficien may e inrduced ake care f i 17. The resuls f numerical mehd using FDM were cmpared wih analyical resuls in my previus wrk where rle f mushy zne in calculains is well descried 1. Wrk is under prgress develp a mdel y numerical mehd fr pure meal cnsidering nly he hea ransfer cnrl.

11 REFERENCES 1. G. Sehi,A.K.Shukla and B De, Thereical aspecs f scrap dissluin in xygen seelmaking cnverers,aistech 4. H.W. Harg, P.J. Kreyger and A.B. Sneijer, C.R.M, N.37, Decemer 1973 pp J. Szekely, Y.K. Chuang and J.W. Hlinka, The meling and dissluin f lw carn irn-carn mels,meallurgical Transacins, 3, 197, pp Y.K. Chuang and J. Szekely, Inernainal Jurnal f Hea and Mass Transfer, 14, 1971, pp E. Spech and R. Jeschar, Seel research, 64, 1993, pp H. Gaye, J. Wanin, P. Gugliermina and P Schily, Prc. 68h Seelmaking Cnference, Deri, U.S.A, April 14-17, 1985, pp H. Yruchu and R. Rlls, Irn and Seel Inernainal, Feruary 1976, pp S. Asai and I. Muchi, Transacins ISIJ, 11, 1971, pp Brahma De, Gaurav Gupa and Manish Gupa, Prc. Asia Seel In. Cnf. Jamshedpur India, April 9-1, Vl., 3, pp..d.1.1-.d G.K. Gupa, B.Tech Repr, Deparmen f Maerials and Meallurgical Engineering, I I T Kanpur, Liuyi Zhang and Franz Oeers, Meling and mixing f allying agens in seel mels, Verlag Sahleisen Gmh, Dusseldrf, 1999, pp Liuyi Zhang and Franz Oeers, Seel Research, 71, N. 5,, pp R.D. Phelke, W.F. Prer, R.F. Uran and J.M. Gains, BOF Seelmaking, Vl., pp E. Kreyszig, Advanced Engineering Mahemaics, Wiley Jhn & Sns, Incrpraed 7h Ediin, Augus J. Szekely, Prcess pimizain, wih applicains in meallurgy and chemical engineering, Wiley, New Yrk, J.P. Hlman, Hea ransfer, 9h ed., McGraw-Hill, New Yrk, 17. J.Krn and H. Fredrikssn, Mdelling f air gap frmain in slidificain prcessing, Trans. Indian Insiue f Meals, 58(4), Augus Manish Mishra, B Tech Thesis, Deparmen f Maerials and Meallurgical Engineering, I I T Kanpur, L.C. Braie and Masahir Kawakami, Kineics f seel scrap melingin mlen Fe-C ah,high Temperaure Maerials and Prcesses, ,19(3-4),..A.K.Verma, Sanjay Chandra and B.K. Dhindaw, A fully implici fixed-grid finie difference frmulain fr phase change prlems, Trans. Indian Insiue f Meals, , 58(4), Augus 5. 1.W.D. Murray and Fred Landis, Numerical and machine sluins f ransien heacnducin prlems invlving meling r freezing Transacins f ASME, 16-11, May 1959.

12 NOMENCLATURE : Nain Descripin Unis Cp Specific Hea f Scrap J/Kg K Wm W f he mel Kg Wscr W f scrap Kg Velciy/v Velciy f mving inerface m/s Time ill Previus ime sep secnds Curren prcess ime secnds Cpm Specific hea f he mel J/Kg K m Densiy f he mel Kg/m3 Thermal diffusiviy f he mel m/s Dc Diffusin Cefficien f Carn in he mel m/s k Thermal cnduciviy f he mel W/m K C Mel ulk Carn cmpsiin % Ci Inerface carn cmpsiin % Cs Scrap cmpsiin a he inerface % Tsci Iniial Scrap Temperaure % Tsc Eig Temperaure inside he scrap a differen lcains Eigen Value K T Mel Bulk Temperaure K T Inerface Temperaure K Hfe Laen hea f slidificain/meling J/Kg h Hea ransfer Cefficien fr fixed undary W/m K h Acual hea ransfer Cefficien W/m K Mass ransfer Cefficien fr fixed undary m/s J ' Acual mass Transfer Cefficien m/s Bessel s funcin f Zer rder J1 Bessels funcin f firs rder i i h r f essels funcin Ciniial Carn cmpsiin f mel a = Tiniial Temperaure f he mel a = r Equilirium rai f carn cmpsiin eween slid and liquid phase Cscrap Cmpsiin f he Paren Scrap %

13 APPENDIX I Esimain f hea and mass ransfer cefficiens fr mving undary The mass ransfer equain in he liquid mel adjacen he he scrap inerface is given as : d C D dx dc v dx [A1] Wih he fllwing undary cndiins : C = Ci a x = C = C a x= c Sluin f he ave equain cmes as fllwing : v k exp( v / k ) c 1 [A] The hea ransfer equain in he liquid mel adjacen he he scrap inerface is given as : d C dc v [A3] dx dx Where D k C p Wih he fllwing undary cndiins : T = Ti a x = T = T a x= Sluin f he ave equain is as fllwing : C pv h exp( C v / h ) 1 p [A4] h

14 APPENDIX B Esimain f aslue value f hea ransfer cefficien as a funcin f inpu energy he seelmaking sysem Fllwing se f mahemaical expressins are used esimae he hea ransfer cefficien where al energy inpu he seel ah is cnsidered under cmined influence f p lance and m sirring sysem : E Q E E E decar decar al E 1 7 d [ C ] 1. W. d Q 6.18 W p Q m.1. cs W decar. T l 6 Q. W. n l.(ln[ 1 E T (ln[ 1 E. M. d. X 3 decar 6. g. H. h _ p. g. H p am ] am [1 frac ] T T l ]) [1 T T l ]) h 5. E al.33 where is he angle f he lance ip frm verical, Q is Oxygen flwrae,w is weigh f seel, n is he numer f penings f he lance, X is he lance heigh ave meal ah during lwing, H is he average heigh f he frmain f CO ules, h_frac is he average deph fracin a which CO ule frmain akes place, d is he hra diameer, T is he Temperaure f he m sirring gas a inpu, T is he average Temperaure f he l liquid Seel, p is he amspheric pressure and h is he hea ransfer cefficien am