Modelling of three dimensional liquid steel flow in continuous casting process

Transcription

1 AMME h Modlling of hr dimnsional liquid sl flow in coninuous casing procss M. Jani, H. Dyja, G. Banasz, S. Brsi Insiu of Modlling and Auomaion of Plasic Woring Procsss, Faculy of Marial procssing Tchnology and Applid Physics, Tchnical Unirsiy of Czsochowa, Al. Armii Krajowj 19, Czsochowa, Poland. In his wor h hory and numrical analysis of fluid flow of liquid sl wr prsnd. Th hr-dimnsional, sady sa, Nwonian and incomprssibl wih urbulncs modl of fluid flow was chosn. Th - modl of urbulnc was usd. For compuaion h sysm ANSYS, which basd on fini lmns mhod, was applid. 1. INTRODUCTION Th simplifid schm of coninuous casing procss in figur 1 was prsnd. Bcaus h sram of liquid sl srongly changs (by lociy fild) h ha xchang by concion, h numrical analysis of fluid flow boh wih hrmal analysis [1] is ry imporan par in modlling of coninuous casing procss. Figur 1. Fragmn of coninuous casr

2 410 M. Jani, H. Dyja, G. Banasz, S. Brsi 2. THEORY Th liquid sl insid h coninuous bill can b ramn as incomprssibl, Nwonian and urbuln fluid. Bhaiour of liquid fluid dscrip following quaions [2,3]: Coninuiy quaion Momnum quaions (Nair Sos quaions) Incomprssibl nrgy quaion Turbulnc modl quaions Th - modl of urbulnc was chosn. This modl is ry popular for modlling liquid sl bhaiour. Th coninuiy quaion is dscrip: ρ ( ρ ) ( ρ ) x y ( ρ z ) = 0 (1) whr: x, y, z - componns of h lociy cor, - dnsiy, x, y, z - global Carsian coordinas, - im. Th ra of chang of dnsiy can b rplacd by h ra of chang of prssur: ρ ρ P = (2) P whr: P prssur. For incomprssibl fluid h quaion (2) can b xprssd as: ρ 1 P = (3) β whr: bul modulus. Th ohr (Nair Sos, nrgy, urbulnc) quaions ha h form of scalar ranspor quaion [2]: ( ρc ) ( ρ C ) ( ρ yc) ( ρ C ) x z = Γ Γ (4) Γ S whr: C - ransin and adcion cofficin, Γ - diffusion cofficin, S - sourc rms. Dscribd cofficins and rms ar prsns in h abl 1. Th rms, which wr no impord for considrd analysis, wr omid. Tabl 1. Transpor quaion rprsnaion Maning C Γ x x lociy 1 y y lociy 1 z z lociy 1 ρ ρ ρ g x g y g z S P P P

3 Modling of hr dimnsional liquid sl flow 411 T mpraur C p K Q inmaic nrgy 1 ε dissipaion ra 1 C T C4β gi x i ρε i 1 x ε C 2ρε i T C C C βg Th abl 1 ha cofficins no dscribd arlir: - dynamic iscosiy, - ffci iscosiy, g x, g y, g z, - componns of acclraion du o graiy K - hrmal conduciiy C p - spcific ha, Q - olumric ha sourc, C 1, C 2, C,,,, C 3, C 4 - sandard -ε modl of urbulnc cofficins (abl 2). Th usd -ε sandard modl cofficins in abl 2 ar prsns. Tabl 2. Usd alus of -ε modl cofficin Cofficin C 1 C 2 C C 3 C 4 Valu Nx sp o numric soluion is discrizaion of h quaions. Th lmns marics ar formd, assmbld and h rsuling sysm sold for ach dgr of frdom sparaly. Th discrizaion procss consis of driing h lmn marics o pu oghr h marix quaion [2]: ransin adcion diffusion ( [ A ] [ ] [ ] ){ φ } = { φ A A S } (5) For lmn ingraion h Galrin mhod of wighd rsiduals is us: [ ] ( ρc φ) ransin φ A = W d( ol) (6) whr: W - wighing funcion for h lmn. adcion [ ] ( ρcφsφ) A = W d( ol) (7) s diffusion [ A ] = ( Wx Γφ Wx Wy Γφ Wy Wz Γφ Wz ) d( ol) (8) whr: φ W xφ = ; W φ φ yφ = ; W z φ = (9,10,11)

4 412 M. Jani, H. Dyja, G. Banasz, S. Brsi W x W = ; W y W = ; W W Sφ z W = (12,13,14) S φ = d(ol ) (15) 3. NUMERICAL SIMULATION For numrical simulaion h paramrs of coninuous casr from mallurgical plan Zawirci in Poland wr usd. Th dimnsions of liquid cor wr an from arlir analysis [4,1]. Th procss and marial paramrs wr prsnd in abl 3. Th oul of h pouring ub was locad 82 mm undr mniscus. Th diamr of pouring ub was 65 mm and diamr of oul 30 mm. Whol liquid cor for considrd cas ha abou 11m. In his wor simulaion for only 1.5 m fragmn of liquid cor was prsnd. Th lociis for xrnal nods wr s o zro. For numrical soluion of quaion 5 h ANSYS fini lmns mhod sysm was usd. Th modl conaind rahdral lmns wih nods. Th figur 2 prsns h fragmn of mshd modl (mniscus rgion). Th graiy acclraion was s o 9.81 m/s 2. Th analysis was sady sa. Tabl 3. Marials propris and casing condiions dnsiy 7080 g/m 3 spcific ha 806 J/gK hrmal conduciiy 30 W/mK dynamic iscosiy g/ms mould dimnsions x x 0.78 m casing spd m/s (1.6 m/min) inl lociy 1 m/s pourd mpraur 1814 K (1541ºC) liquidus mpraur 1784 K (1511ºC) Figur 2. Fragmn of mshd modl (mniscus rgion)

5 Modling of hr dimnsional liquid sl flow 413 a) b) 1,2 Summary locis in h cnr of bill (m/s) 1 0,8 0,6 0,4 0, ,2 0,4 0,6 0,8 1 1,2 1,4 Disanc from mniscus (m) c) 0,2 Vlocis in h cross scion of bill (m/s) 0-0,2-0,4-0,6-0, m 0.25 m 0.5 m 0.75 m 1 m 1.25 m -1,2 0 0,025 0,05 0,075 0,1 0,125 0,15 Disanc from lf dg of bill (m) Figur 3. Compud rsuls, a) lociy fild in h fragmn of longiudinal scion, b) summary lociis in h cnr of bill, c) profils of lociy in cross scion of bill for arious disancs from mniscus

6 414 M. Jani, H. Dyja, G. Banasz, S. Brsi Th compud fild of lociy cors in figur 3a was showd. Th maximum alus of lociis in h cnr of bill in figur 3b wr prsnd. Th profils of lociy for arious disancs from mniscus in figur 3c wr showd. Th maximum rang of h sram of liquid sl can b drmind as 1.1 m. Also bwn mniscus and 1.1 m is locad h rgion of maximum mixing of mal. Thrfor h conci ffcs of ranspor of ha rach maximum alus for his rgion. Simulaion of whol liquid cor (from mniscus o unbnding poin - abou 11m) rquird high compur powr. In cas of only simulaion rgion of high mixing, h cos of compuaion quicly dcrasing. REFERENCES 1. M. Jani, H. Dyja.: Modlling of hr dimnsional hrmal fild in mould during coninuous casing of sl. Achimns in Mchanical and Marials Enginring AMME Gliwic Zaopan, Poland, ANSYS, Inc. Thory Rfrnc R. Grybo.: Podsawy mchanii płynów. PWN, Warszawa M. Jani, H. Dyja, S. Brsi, G. Banasz.: Two dimnsional hrmomchanical analysis of coninuous casing procss. Inrnaional Confrnc on Adancd in Marials and Procssing Tchnologis - AMPT Dublin, Irland 2003.