METHOD FOR DETERMINING THE THERMAL BOUNDARY CONDITION IN THE CC MOULD FOR NUMERIC MODELS. René PYSZKO, Miroslav PŘÍHODA, Marek VELIČKA

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1 8.. 5., Roznov pod Rdhostem, Czech Republc, EU METHOD FOR DETERMINING THE THERMAL BOUNDARY CONDITION IN THE CC MOULD FOR NUMERIC MODELS Abstrkt René PYSZKO, Mroslv PŘÍHODA, Mrek VELIČKA VŠB-TU Ostrv, 7. lstopdu 5, Ostrv - Porub, Česká republk, rene.pyszko@vsb.cz The pper dels th the methodology of determnton the boundry condtons n contnuous cstng mould for the purpose of numercl modellng. Most relevnt s het trnsport n drecton perpendculrly to the strnd surfce. The most commonly used s condton of nd knd tht s het flux prtculrly n the cses here model does not nclude mould. If model contns mould, other types of surfce condtons cn be specfed, such s condton of 3 rd type for het trnsport from the strnd surfce through lyer of lubrcnt, gs gp, copper plte to the coolng ter by convecton. Number of unknon prmeters n ths cse s lrge nd the condton s loded th n uncertnty of het resstnce n the gp. Wheres, n plnt, tempertures nd flo rte of the coolng ter n mould re typclly mesured, the totl het flux from steel to coolng ter cn be esy found. The vlue of het flo nto the coolng ter determned n ths y s suffcently precse nd chrcterzes globl ntensty of the prmry coolng, but t s nsuffcent for descrpton of lyout of het flux n the mould lls. In order to dvde the globl het flo nto ll lls nd dstrbute t long the heght of the lls, lrge dtbse of mesurement usng n expermentl mould, hch s equpped th thermocouples n copper lls, hs been used. From the mesured tempertures s, by mens of polynoml nd splne nterpolton, derved dstrbuton of het flux long the mould heght. Influences of cstng speed nd steel chemcl composton on het flux n the mould hs been nlyzed.. INTRODUCTION Therml models of soldfyng bllets t contnuous cstng mchnes (CCM) re used for both the reserch tsks, s ell s the cstng process control support. The gol s to clculte the temperture feld of the strnd, the thckness of sold shell nd the metllurgcl length. Intensty nd unformty of het removl n the ndvdul segments of cstng mchnes re ssocted th both surfce nd nternl qulty of bllets. The clculted temperture felds re lso used s nput nformton for mult-physcl modellng of steel flong n the mould, stress nlyss of mould [4], [8] nd strnd, chemcl heterogenetes [9] nd crckng ndex. Temperture felds cn be smulted by off-lne or on-lne models. Models of the second type re nformton-lnked to the contnuous cstng process control system nd set the boundry condtons th regrd to the mmedte dynmc chnges of cstng prmeters. Ths type of therml models my be prt of dgnostcs system, hose lgorthms use temperture felds to ncrese the success of qulty nd brekout predcton [6], [7], [], []. In cse of off-lne models, the communcton th control system s replced by selectng the process prmeters from dtbse of mesured vlues or boundry condtons re determned from knon dependences n form of mthemtcl equtons [] or sttstcl models [], [3]. The pper focuses on therml boundry condtons n mould of bllet cster. The term boundry condton of frst type mens surfce temperture, the condton of the second knd s used for het flux nd the thrd type ndctes convecton nd rdton. On the steel level n mould the

2 8.. 5., Roznov pod Rdhostem, Czech Republc, EU boundry condton of the frst type, hch represents the temperture of the lqud steel, s entered. A dfferent condton of het removl t ths boundry could be lso entered, hch ould chrcterze the ctul physcl process n more ccurte y, e.g. the combnton of convecton zone nd rdton. But such condton hs consderble uncertnty for lck of knoledge of the het trnsport through lyer of lubrcnt, hose thckness vres. Therml conductvty of lubrcnt s not knon s ell s emssvty dependng on temperture nd phse. On the lterl surfce of the emergng bllet n the mould the second knd of boundry condton s specfed,.e. het flux. Here other knd of surfce condtons cn be used, such s compound condton of the thrd type for het flo from the bllet surfce through lqud nd sold phses of lubrcnt, gs gp, nd copper plte to the coolng ter, but the number of unknon prmeters n ths cse s too lrge. Other het flos n the mould cn be neglected. For exmple, het conducton from the copper lls to the mould frme nd to surroundngs []. To determne the boundry condtons for off-lne model, dtbse of mesurement results s used. The expermentl mesurng s crred out on bllet CCM of formt 5 x 5 mm, durng hch there ere recorded, n ddton to opertng prmeters, tempertures n the lls of speclly modfed mould nd output vrbles from dgnostcs nd brekout predcton system DGS [3], []. Acqured dtbse contns 387 hets, from hch there ere found n totl 85 qus-stedy ntervls, ech 8.5 mnutes long. The verge vlues of qunttes thn the ntervls ere ssessed. Qus-stedy ntervls re defned by cstng speed, hch s not dverted by more thn specfed lmt. Cstng speed n dtbse rnges from.88 to.85 m mn - ; crbon content of steels s thn n ntervl from,8 to,6 t%. The dtbse contns dt from cstng both th the submerged entry nozzle (SEN) nd thout nozzle.. DETERMINATION OF HEAT FLOW FROM THE MOULD TO COOLING WATER Wheres, the mould coolng ter temperture nd flo rte re mesured t the plnt, t s esy to determne het flo from steel to ter. The follong equton s used P ( c t c t ) = ρ Q (W) () p, p, here ρ (kg.m -3 ) s ter densty t the pont of flo rte mesurng, Q (m 3.s - ) s mesured ter flo rte, c p,, c p, (J.kg -.K - ) re men specfc hets nd t, t ( C) re tempertures of nlet nd outlet coolng ter. Het flo dependence on cstng speed nd crbon content s shon n the fgure s surfce chrt from ll 85 dt ponts. All dt ponts re verge vlues of qus-stedy ntervls. The globl verge het flo from ll dt s.933 MW. Mxml het flo up to. MW cn be observed for cstng speed rngng from.7 to.4 m.mn - nd crbon content from,75 up to,9 t% C, hch ere cst thout SEN. The loest het flos belo.7 MW ere mesured n cses of crbon content close to,83 t%, throughout the complete rnge of cstng speeds; there s consderble furro n the chrt. Problems th lrge shrnkge nd unstedy behvour of the process hen cstng these steels re generlly knon. For lo crbon steels th crbon content belo.8 t%, hch ere cst th SEN, het flos rse over the verge vlue. Durng cstng steels th crbon exceedng,8 t% het flo s hgher thn verge, but for crbon over,87 % het flo drops belo the verge. The globl trend for ll dt ponts shos tht het flo n the mould rses th ncresng crbon nd th the groth of cstng speed.

3 8.. 5., Roznov pod Rdhostem, Czech Republc, EU Fg.. Globl het flo from the mould to the coolng ter 3. LAYOUT OF HEAT FLUX IN THE MOULD WALLS Het flo to the coolng ter chrcterzes globlly the het removl n mould, but t s not suffcent for the descrpton of the het flux lyout on the mould lls. Het flux lyout n rel mould s qute uneven, both n the drecton of cstng nd cross-se. Het flux lso vres n tme due to perodc chnges of contct beteen the shell nd the mould ll, for uneven lubrcnt dstrbuton nd becuse of fluctutng cstng prmeters, mnly the cstng speed. Obtnng ccurte mmedte vlues of locl het flux s technclly dffcult. Usully t s endevourng to obtn t lest the verge locl het flux vlues n qus-sttonry stte. Het flux n the mould lls cn be mesured usng prs of thermocouples, hch must be plced t dfferent ccurte dstnces from the ork surfce. As the nstrumentton of thermocouples prs s technclly demndng nd expensve they ere replced by mesurng the ll tempertures by sngle thermocouples.. Evlutng het flux n the mould lls It s possble, hle cceptng severl smplfctons, to evlute locl het flux n the ll from the mesured ll temperture nd coolng ter temperture t t = s λ + α m q (W.m - ) () here λ (W.m -.K - ) s het conductvty of the copper ll, s (m) s dstnce beteen the thermocouple nd the cooled surfce, t m ( C) s mesured temperture n the ll, t ( C) s ter temperture t the level of thermocouple, α (W.m -.K - ) s het trnsfer coeffcent beteen the cooled surfce nd the coolng ter, hch cn be clculted usng Reynolds nd Prndtl numbers nd crter equton.

4 8.. 5., Roznov pod Rdhostem, Czech Republc, EU Thus, only locl het flux t the thermocouple poston cn be clculted. Vlues t other postons must be computed usng nterpolton or extrpolton, hch cuses errors. Therefore, t s preferble to use combnton of mesurng ll tempertures technque th the mesurement of het flo to the coolng ter. Fg.. Thermocouples n the mould In lmted rnge of tempertures, the vlue of mould ll het conductvty nd het trnsfer coeffcent beteen the mould surfce nd coolng ter cn be ssumed constnt. Het flux cn be expressed by lner functon of temperture dfference beteen mesured ll temperture nd ter temperture t the level of thermocouple ( ) q = K t m t (W.m - ) (3) here K (W.m -.K - ) s equvlent to men het trnsfer coeffcent beteen thermocouple poston n the ll nd coolng ter. Wter temperture s ssumed to rse lnerly long the ll length. Durng the expermentl mesurement the thermocouples ere nstlled t fve dscrete ponts t longtudnl xs of ech ll. A temperture dfference beteen the ll temperture nd ter temperture t m, = t t cn be pproxmted by polynoml functon of the 5 th order dependng on reltve mould m length z r () 5 m,,5 zr , zr, t = + ( C) (4) here s n ndex of the ll. Closer pproxmton cn be obtned by cubc splne curve 3 ( zr zr, ) + +,, ( zr zr, ), t m,,3,... +, = ( C) (5) here s n ndex of ntervls beteen temperture mesurng ponts, nd z r, () s reltve coordnte of temperture mesurng pont. Addtonl fctve temperture ponts ere dded t the steel level nd t the bottom of the mould by lner extrpolton thus there re 7 temperture ponts or 6 length ntervls long the mould heght. The globl het flo through the ll s clculted by ntegrton P = K B t m, dz (W) (6) r After substtuton of the polynoml functon of the 5 th order e obtn,5, P = K B + + +, (W) (7) 6 The sum of the het flo through ll four lls should be equl to the het flo to coolng ter

5 8.. 5., Roznov pod Rdhostem, Czech Republc, EU 4 P = P (W) (8) = nd then the coeffcent K cn be clculted from the formul ρ Q K = 4 B = 6 ( c t c t ),5 p, + + p,, +, (W.m -.K - ) (9) nd fnly het flux n the ll of n ndex cn be clculted from the equton 4 ( z + + z ) q = K + (W.m - ) (), 5 r..., r, Whle usng splne functon the formuls of boundry condtons re more complex becuse dfferent polynomls re used for ech ntervl 3 ( ( z z ) + + ( z z ) ) q K, 3, r r,...,, r r, +,, = (W.m - ) () The equtons () or () cn be used n therml numercl models s boundry condtons n the mould.. Progrm code for clculton the boundry condton The bove descrbed method s embedded nto the orgnl progrm code for Mtlb, hch clcultes boundry condtons n the mould for optonl cstng prmeters usng the dtbse of mesured dt. The outputs of the progrm re, besdes grphcl results, numercl sets of prmeters of polynoml functon of the 5 th order nd splne functons of het flux n dependence on reltve coordnte z r for ech of four lls. The progrm s used th softre system Procst t the deprtment of therml engneerng, VŠB-TU Ostrv. A smlr lgorthm s used n n on-lne model of round block contnuous cstng, hch s developed t the deprtment [5], [7]. The clculted profles of het flux for selected prmeters re shon s exmple outputs. The fgures 3 nd 4 compre het flux profles of lo crbon steel th crbon content less thn,8 t% nd hgh crbon steel th t%. In the fgures 5 nd 6 het flux profles of hgher cstng speed re compred th loer cstng speed, n both cses there s the sme crbon content. -. t%. Crbon content hs hgher nfluence on the het flux profle thn cstng speed. There s sgnfcnt dfference beteen profles t dfferent lls. Het flux t the nner rdl ll (IR) hs typcl profle of S-shpe by contrst to other lls. The lbels of lls used n fgures 3 to 6 men IR - nner rdus, OR - outer rdus, LS -.left sde, RS rght sde.

6 8.. 5., Roznov pod Rdhostem, Czech Republc, EU.5.5 q (MW.m - ).5 q (MW.m - ) reltve length () reltve length () Fg. 3. Lo crbon steel -.8 t% C Fg. 4. Hgh crbon steel t% C.5.5 q (MW.m - ).5 q (MW.m - ) reltve length () reltve length () Fg. 5. Cstng speed.8. m.mn -,. -. t% C Fg. 6. Cstng speed.6.9 m.mn -,. -. t% C 4. CONCLUSIONS A dtbse from n-plnt mesurement durng cstng of 387 hets s used for determnton of boundry condtons n mould. Globl het flo to coolng ter s clculted from ter tempertures nd flo rte. Mxml het flo up to. MW cn be observed for cstng speed rngng from.7 to.4 m.mn - nd crbon content from,75 up to,9 t% hle cstng thout SEN. The loest het flos belo.7 MW ere found n cses of crbon content close to,83 t%. The globl trend for ll dt ponts shos tht het flo n the mould rses th ncresng crbon content nd groth of cstng speed. A method for evluton of het flux lyout n the mould lls, hch s bsed on mesurng ll tempertures by thermocouples, s developed. Het flux profles re obtned s polynoml or splne functons n dependence on reltve mould length. The method s embedded nto the orgnl progrm code for Mtlb. The progrm s used th softre system Procst t the deprtment of therml engneerng, VŠB-TU

7 8.. 5., Roznov pod Rdhostem, Czech Republc, EU Ostrv. Smlr lgorthm s used n n on-lne model of round block contnuous cstng, hch s developed t the deprtment. Crbon content hs hgher nfluence on the het flux profle shpe thn cstng speed. There s sgnfcnt dfference beteen profles t dfferent lls. Het flux t the nner rdl ll hs typcl profle of S-shpe by contrst to other lls. ACKNOWLEDGMENTS The uthors thnk the compnes Třnecké železárny,.s. for contrbuton of n-plnt dt nd DASFOS, v.o.s. for dt mesurng nd pre-processng. Ths reserch hs been supported by grnts of MPO No. FT-TA4/48 nd GAČR No. GA6/7/938. LITERATURE [] VELIČKA, M. et l. Reserch of het trnsport n mould for contnuous cstng of steel. Metlurg, December 9, No. 4, p ISSN [] ŠTĚTINA, J. et l. Het trnsfer coeffcents beneth the ter coolng nozzles of bllet cster. In the Conference Proceedngs Tnger Ostrv, Tnger s.r.o., 9, p. -9, ISBN [3] MAUDER, T. et l. Mthemtcl & Stochstc modellng of the concstng of steel slbs. In the Conference Proceedngs Tnger Ostrv, Tnger s.r.o., 9, p. 4-48, ISBN [4] FRYDRÝŠEK, K.: Řešení problemtky nestconární, cyklcké, tepelné elstoplstcké nptost v krystlzátoru pro plynulé odlévání. Ostrv: VŠB-TU Ostrv, Česká republk, 9, pp.4. ISBN [5] PŘÍHODA, M. et l. Numercl model of soldfcton of round strnd for on-lne montorng. Hutncké lsty, LXI, 8, No., p ISSN [6] POKORNÝ, M., FOJTÍK, P. Complex systems dgnoss usng fuzzy non-lner modellng. In Proceedngs of 4th Interntonl Congress of Cybernetcs nd systems of WOSC. 4th Interntonl Congress of Cybernetcs nd systems of WOSC. Wrocl, Polnd: Ofcn Wydncz Poltechnk Wroclske, 8, pp ISBN [7] PYSZKO, R., FOJTÍK, Z., ADAMIK, M. Montorng nd Brekout Predcton System th Integrted On-lne Numercl Model DGS-DMT for Contnuous Cstng Mchne Formt D55. Act Metllurgc Slovc, vol. 3, no. 5/7 (specl ssue), p ISSN [8] FRYDRÝŠEK, K. et. l. Trnsent Therml Stress-Strn Sttes n the Mold for Contnuous Cstng, In: Book of Extended Abstrcts 45th Interntonl Conference "Expermentl Stress Anlyss 7", ISBN , Fculty of Appled Scences, Unversty of West Bohem n Plsen nd Czech Socety for Mechncs, Plzeň, 7, Czech Republc, pp.33-34, (full verson lso on CD). RIV/6989:73/7:4844 [9] KAVIČKA, F. et l. The optmzton of concstng technology by to numercl models. Journl of Mterls Processng technology 85 (7), p [] PYSZKO, R. et l. Numercl model for temperture feld knetcs for round strnds. In Proceedngs of st Interntonl Conference STEELSIM October 5, Brno, p. ISBN [] PYSZKO, R. et l. Advnced Process Montorng Systems for Contnuous Processes. In The 6th IFAC World Congress. July Prgue. Czech republc [CD ROM]. Prgue: CVUT: July, 5, Pper code: Th-E4-TO/4. 6 p. [] PŘÍIHODA, M. et l. Prncples of the shell groth n CC mould. Hutncké lsty. LVII,, No. 4 5, p ISSN